JEE MAIN · MATHEMATICS · PROBABILITY
JEE Main Probability Questions & Solutions
143 solved questions on Probability, ranging from easy to JEE-Advanced-flavour hard. Click any to see the full solution.
143 solved questions on Probability, ranging from easy to JEE-Advanced-flavour hard. Click any to see the full solution.
Let X be a random variable having binomial distribution B(7, p). If P(X = 3) = 5P(x = 4), then the sum of the mean and the variance of X is :
View solution →Let X have a binomial distribution B(n, p) such that the sum and the product of the mean and variance of X are 24 and 128 respectively. If $P(Xn-3)=\frac{k}{2^{n}}$, then k is…
View solution →Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random and a ball is drawn from it. If the ball…
View solution →If a random variable X follows the Binomial distribution B(5, p) such that P(X = 0) = P(X = 1), then ${{P(X = 2)} \over {P(X = 3)}}$ is equal to :
View solution →Let a die be rolled $n$ times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting…
View solution →Let E1 and E2 be two events such that the conditional probabilities $P({E_1}|{E_2}) = {1 \over 2}$, $P({E_2}|{E_1}) = {3 \over 4}$ and $P({E_1} \cap {E_2}) = {1 \over 8}$. Then :
View solution →A random variable X has the following probability distribution : .tg {border-collapse:collapse;border-spacing:0;} .tg…
View solution →If an unbiased die, marked with $-2,-1,0,1,2,3$ on its faces, is thrown five times, then the probability that the product of the outcomes is positive, is :
View solution →Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be ${1 \over 2}$ and probability of…
View solution →If the probability that the random variable $\mathrm{X}$ takes values $x$ is given by $\mathrm{P}(\mathrm{X}=x)=\mathrm{k}(x+1) 3^{-x}, x=0,1,2,3, \ldots$, where $\mathrm{k}$ is a…
View solution →When a missile is fired from a ship, the probability that it is intercepted is ${1 \over 3}$ and the probability that the missile hits the target, given that it is not…
View solution →If the probability that a randomly chosen 6-digit number formed by using digits 1 and 8 only is a multiple of 21 is p, then 96 p is equal to _______________.
View solution →In a workshop, there are five machines and the probability of any one of them to be out of service on a day is ${{1 \over 4}}$ . If the probability that at most two machines will…
View solution →The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to :
View solution →The probability distribution of random variable X is given by : .tg {border-collapse:collapse;border-spacing:0;} .tg…
View solution →Let A and B be two events such that the probability that exactly one of them occurs is ${2 \over 5}$ and the probability that A or B occurs is ${1 \over 2}$ , then the probability…
View solution →A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n is ${1 \over n}$. If the die is thrown thrice, then the…
View solution →An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value of k when k consecutive heads are obtained for k = 3, 4, 5, otherwise X takes the value -1.…
View solution →Each of the persons A and B independently tosses three fair coins. The probability that both of them get the same number of heads is :
View solution →If the sum and the product of mean and variance of a binomial distribution are 24 and 128 respectively, then the probability of one or two successes is :
View solution →Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is :
View solution →From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable $X$ denote the number of defective items in the sample. Let items…
View solution →From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random. Let the random variable $X$ denote the number of defective items in the sample. If…
View solution →An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability, that the first draw gives all white balls and the second…
View solution →A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is :
View solution →Let Bi (i = 1, 2, 3) be three independent events in a sample space. The probability that only B1 occur is $\alpha$, only B2 occurs is $\beta$ and only B3 occurs is $\gamma$. Let p…
View solution →Let A and B be two independent events such that P(A) = ${1 \over 3}$ and P(B) = ${1 \over 6}$. Then, which of the following is TRUE?
View solution →Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3. Then probability of event A is equal to :
View solution →The probability that a randomly chosen 5-digit number is made from exactly two digits is :
View solution →An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then…
View solution →Let $\mathrm{a}, \mathrm{b}$ and $\mathrm{c}$ denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked $1,2,3,4$. If the probability…
View solution →If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $i^{\text {th }}$ roll than the number obtained in the $(i-1)^{\text {th }}$ roll,…
View solution →In a bolt factory, machines $A, B$ and $C$ manufacture respectively $20 \%, 30 \%$ and $50 \%$ of the total bolts. Of their output 3, 4 and 2 percent are respectively defective…
View solution →Let S = {E1, E2, ........., E8} be a sample space of a random experiment such that $P({E_n}) = {n \over {36}}$ for every n = 1, 2, ........, 8. Then the number of elements in the…
View solution →An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is 0.9 and that of…
View solution →The coefficients a, b and c of the quadratic equation, ax2 + bx + c = 0 are obtained by throwing a dice three times. The probability that this equation has equal roots is :
View solution →When a certain biased die is rolled, a particular face occurs with probability ${1 \over 6} - x$ and its opposite face occurs with probability ${1 \over 6} + x$. All other faces…
View solution →One die has two faces marked 1 , two faces marked 2 , one face marked 3 and one face marked 4 . Another die has one face marked 1 , two faces marked 2 , two faces marked 3 and one…
View solution →The probability of selecting integers a$\in$[$-$ 5, 30] such that x2 + 2(a + 4)x $-$ 5a + 64 > 0, for all x$\in$R, is :
View solution →A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let $\mathrm{X}$ be the number of white balls, among the drawn balls. If $\sigma^{2}$ is…
View solution →If the mean of the following probability distribution of a radam variable $\mathrm{X}$ : .tg {border-collapse:collapse;border-spacing:0;} .tg…
View solution →Let $\mathrm{E}_{1}, \mathrm{E}_{2}, \mathrm{E}_{3}$ be three mutually exclusive events such that $$\mathrm{P}\left(\mathrm{E}_{1}\right)=\frac{2+3 \mathrm{p}}{6},…
View solution →A random variable X has the following probability distribution : .tg {border-collapse:collapse;border-spacing:0;width:100%} .tg td{font-family:Arial,…
View solution →Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from…
View solution →Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is :
View solution →Let A be a set of all 4-digit natural numbers whose exactly one digit is 7. Then the probability that a randomly chosen element of A leaves remainder 2 when divided by 5 is :
View solution →Five numbers ${x_1},{x_2},{x_3},{x_4},{x_5}$ are randomly selected from the numbers 1, 2, 3, ......., 18 and are arranged in the increasing order $({x_1}
View solution →Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at…
View solution →A fair $n(n 1)$ faces die is rolled repeatedly until a number less than $n$ appears. If the mean of the number of tosses required is $\frac{n}{9}$, then $n$ is equal to…
View solution →The coefficients $\mathrm{a}, \mathrm{b}, \mathrm{c}$ in the quadratic equation $\mathrm{a} x^2+\mathrm{bx}+\mathrm{c}=0$ are from the set $\{1,2,3,4,5,6\}$. If the probability of…
View solution →A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is :
View solution →The probabilities of three events A, B and C are given by P(A) = 0.6, P(B) = 0.4 and P(C) = 0.5. If P(A$\cup$B) = 0.8, P(A$\cap$C) = 0.3, P(A$\cap$B$\cap$C) = 0.2, P(B$\cap$C) =…
View solution →If a random variable X follows the Binomial distribution B(33, p) such that $3P(X = 0) = P(X = 1)$, then the value of ${{P(X = 15)} \over {P(X = 18)}} - {{P(X = 16)} \over {P(X =…
View solution →A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is
View solution →Let $S=\{1,2,3, \ldots, 2022\}$. Then the probability, that a randomly chosen number n from the set S such that $\mathrm{HCF}\,(\mathrm{n}, 2022)=1$, is :
View solution →Let $S$ be the sample space of all five digit numbers. It $p$ is the probability that a randomly selected number from $S$, is a multiple of 7 but not divisible by 5 , then $9 p$…
View solution →Let X be a random variable such that the probability function of a distribution is given by $P(X = 0) = {1 \over 2},P(X = j) = {1 \over {{3^j}}}(j = 1,2,3,...,\infty )$. Then the…
View solution →In an examination, there are 10 true-false type questions. Out of 10, a student can guess the answer of 4 questions correctly with probability ${3 \over 4}$ and the remaining 6…
View solution →Out of $60 \%$ female and $40 \%$ male candidates appearing in an exam, $60 \%$ candidates qualify it. The number of females qualifying the exam is twice the number of males…
View solution →There are three bags $X, Y$ and $Z$. Bag $X$ contains 5 one-rupee coins and 4 five-rupee coins; Bag $Y$ contains 4 one-rupee coins and 5 five-rupee coins and Bag $Z$ contains 3…
View solution →If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is :
View solution →Three dice are rolled. If the probability of getting different numbers on the three dice is $\frac{p}{q}$, where $p$ and $q$ are co-prime, then $q-p$ is equal to :
View solution →Let $$S=\left\{M=\left[a_{i j}\right], a_{i j} \in\{0,1,2\}, 1 \leq i, j \leq 2\right\}$$ be a sample space and $A=\{M \in S: M$ is invertible $\}$ be an event. Then $P(A)$ is…
View solution →Three distinct numbers are selected randomly from the set $\{1,2,3, \ldots, 40\}$. If the probability, that the selected numbers are in an increasing G.P., is $\frac{m}{n},…
View solution →In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and vegetarian. Their chances of getting a…
View solution →A six faced die is biased such that $3 \times \mathrm{P}($a prime number$)\,=6 \times \mathrm{P}($a composite number$)\,=2 \times \mathrm{P}(1)$. Let X be a random variable that…
View solution →An integer is chosen at random from the integers $1,2,3, \ldots, 50$. The probability that the chosen integer is a multiple of atleast one of 4, 6 and 7 is
View solution →The probability of a man hitting a target is ${1 \over {10}}$. The least number of shots required, so that the probability of his hitting the target at least once is greater than…
View solution →Let A, B and C be three events such that the probability that exactly one of A and B occurs is (1 $-$ k), the probability that exactly one of B and C occurs is (1 $-$ 2k), the…
View solution →Let $X$ be a binomially distributed random variable with mean 4 and variance $\frac{4}{3}$. Then, $54 \,P(X \leq 2)$ is equal to :
View solution →A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to probability of getting 9 heads, then the probability of getting 2 heads is :
View solution →A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is
View solution →Let M be the maximum value of the product of two positive integers when their sum is 66. Let the sample space $S = \left\{ {x \in \mathbb{Z}:x(66 - x) \ge {5 \over 9}M} \right\}$…
View solution →A fair die is tossed until six is obtained on it. Let x be the number of required tosses, then the conditional probability P(x $\ge$ 5 | x > 2) is :
View solution →The probability that two randomly selected subsets of the set {1, 2, 3, 4, 5} have exactly two elements in their intersection, is :
View solution →Let N denote the sum of the numbers obtained when two dice are rolled. If the probability that ${2^N}
View solution →If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly two addresses is :
View solution →A bag contains 19 unbiased coins and one coin with head on both sides. One coin drawn at random is tossed and head turns up. If the probability that the drawn coin was unbiased,…
View solution →A bag contains 6 white and 4 black balls. A die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability…
View solution →In a tournament, a team plays 10 matches with probabilities of winning and losing each match as $\frac{1}{3}$ and $\frac{2}{3}$ respectively. Let $x$ be the number of matches that…
View solution →Let $\mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}\right]$ be a square matrix of order 2 with entries either 0 or 1 . Let E be the event that A is an invertible matrix. Then the…
View solution →Let A and B be independent events such that P(A) = p, P(B) = 2p. The largest value of p, for which P (exactly one of A, B occurs) = ${5 \over 9}$, is :
View solution →Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that $N-2,\sqrt{3N},N+2$ are in geometric progression be $\frac{k}{48}$. Then the…
View solution →Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, one word is selected at random. The probability that the…
View solution →Let 9 distinct balls be distributed among 4 boxes, B1, B2, B3 and B4. If the probability than B3 contains exactly 3 balls is $k{\left( {{3 \over 4}} \right)^9}$ then k lies in the…
View solution →Let X be a random variable with distribution. .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial,…
View solution →The probability that a randomly selected 2-digit number belongs to the set {n $\in$ N : (2n $-$ 2) is a multiple of 3} is equal to :
View solution →A dice is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared atleast…
View solution →A student appeared in an examination consisting of 8 true-false type questions. The student guesses the answers with equal probability. the smallest value of n, so that the…
View solution →Two fair dice are thrown. The numbers on them are taken as $\lambda$ and $\mu$, and a system of linear equationsx + y + z = 5x + 2y + 3z = $\mu$ x + 3y + $\lambda$z = 1is…
View solution →In a bombing attack, there is 50% chance that a bomb will hit the target. Atleast two independent hits are required to destroy the target completely. Then the minimum number of…
View solution →Let there be three independent events E1, E2 and E3. The probability that only E1 occurs is $\alpha$, only E2 occurs is $\beta$ and only E3 occurs is $\gamma$. Let 'p' denote the…
View solution →In a box, there are 20 cards, out of which 10 are lebelled as A and the remaining 10 are labelled as B. Cards are drawn at random, one after the other and with replacement, till a…
View solution →Let $\mathrm{A}$ and $\mathrm{B}$ be two events such that $P(B \mid A)=\frac{2}{5}, P(A \mid B)=\frac{1}{7}$ and $P(A \cap B)=\frac{1}{9} \cdot$ Consider (S1) $P\left(A^{\prime}…
View solution →The probability that a randomly chosen one-one function from the set {a, b, c, d} to the set {1, 2, 3, 4, 5} satisfies f(a) + 2f(b) $-$ f(c) = f(d) is :
View solution →Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048 respectively. Then the probability of getting…
View solution →The mean and variance of a binomial distribution are $\alpha$ and $\frac{\alpha}{3}$ respectively. If $\mathrm{P}(X=1)=\frac{4}{243}$, then $\mathrm{P}(X=4$ or 5$)$ is equal to :
View solution →Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations $x + y + z = 1$ $2x + \mathrm{N}y + 2z = 2$ $3x + 3y + \mathrm{N}z…
View solution →The random variable $\mathrm{X}$ follows binomial distribution $\mathrm{B}(\mathrm{n}, \mathrm{p})$, for which the difference of the mean and the variance is 1 . If $2…
View solution →If the numbers appeared on the two throws of a fair six faced die are $\alpha$ and $\beta$, then the probability that $x^{2}+\alpha x+\beta0$, for all $x \in \mathbf{R}$, is :
View solution →Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable $x$ to be the number of rotten apples in a draw of two apples, the variance of $x$…
View solution →Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 $\times$ 2 matrices. The probability that such formed matrix have all different entries…
View solution →Two integers $x$ and $y$ are chosen with replacement from the set $\{0,1,2,3, \ldots, 10\}$. Then the probability that $|x-y|5$, is :
View solution →Two dice A and B are rolled. Let the numbers obtained on A and B be $\alpha$ and $\beta$ respectively. If the variance of $\alpha-\beta$ is $\frac{p}{q}$, where $p$ and $q$ are…
View solution →In a binomial distribution $B(n,p)$, the sum and the product of the mean and the variance are 5 and 6 respectively, then $6(n+p-q)$ is equal to :
View solution →A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p. Next four balls…
View solution →Two dice are thrown independently. Let $\mathrm{A}$ be the event that the number appeared on the $1^{\text {st }}$ die is less than the number appeared on the $2^{\text {nd }}$…
View solution →Let $\mathrm{S} = \{ {w_1},{w_2},......\}$ be the sample space associated to a random experiment. Let $P({w_n}) = {{P({w_{n - 1}})} \over 2},n \ge 2$. Let $A = \{ 2k + 3l:k,l \in…
View solution →The sum and product of the mean and variance of a binomial distribution are 82.5 and 1350 respectively. Then the number of trials in the binomial distribution is ____________.
View solution →Let EC denote the complement of an event E. Let E1 , E2 and E3 be any pairwise independent events with P(E1) > 0 and P(E1 $\cap$ E2 $\cap$ E3) = 0. Then P($E_2^C \cap…
View solution →The probability that a randomly chosen 2 $\times$ 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to :
View solution →In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two dice, in each throw is noted. A wins the game if he…
View solution →The coefficients $a, b, c$ in the quadratic equation $a x^2+b x+c=0$ are chosen from the set $\{1,2,3,4,5,6,7,8\}$. The probability of this equation having repeated roots is :
View solution →25% of the population are smokers. A smoker has 27 times more chances to develop lung cancer than a non smoker. A person is diagnosed with lung cancer and the probability that…
View solution →Let $\Omega$ be the sample space and $\mathrm{A \subseteq \Omega}$ be an event. Given below are two statements : (S1) : If P(A) = 0, then A = $\phi$ (S2) : If P(A) = 1, then A =…
View solution →Two dies are rolled. If both dices have six faces numbered 1, 2, 3, 5, 7 and 11, then the probability that the sum of the numbers on the top faces is less than or equal to 8 is :
View solution →Let S = {1, 2, 3, 4, 5, 6}. Then the probability that a randomly chosen onto function g from S to S satisfies g(3) = 2g(1) is :
View solution →Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then the probability of getting atmost two heads is :
View solution →Let the probability of getting head for a biased coin be $\frac{1}{4}$. It is tossed repeatedly until a head appears. Let $\mathrm{N}$ be the number of tosses required. If the…
View solution →Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing. Then the probability,…
View solution →Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables $X$ and $Y$ respectively denote the number of blue and yellow balls. If…
View solution →A fair coin is tossed n-times such that the probability of getting at least one head is at least 0.9. Then the minimum value of n is ______________.
View solution →A pair of dice is thrown 5 times. For each throw, a total of 5 is considered a success. If the probability of at least 4 successes is $\frac{k}{3^{11}}$, then $k$ is equal to :
View solution →A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If $\mathrm{X}$ denotes the number of tosses of the…
View solution →Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found…
View solution →A company has two plants $A$ and $B$ to manufacture motorcycles. $60 \%$ motorcycles are manufactured at plant $A$ and the remaining are manufactured at plant $B .80 \%$ of the…
View solution →A fair die is tossed repeatedly until a six is obtained. Let $X$ denote the number of tosses required and let $a=P(X=3), b=P(X \geqslant 3)$ and $c=P(X \geqslant 6 \mid X3)$. Then…
View solution →A card from a pack of 52 cards is lost. From the remaining 51 cards, n cards are drawn and are found to be spades. If the probability of the lost card to be a spade is…
View solution →A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are…
View solution →Let Ajay will not appear in JEE exam with probability $\mathrm{p}=\frac{2}{7}$, while both Ajay and Vijay will appear in the exam with probability $\mathrm{q}=\frac{1}{5}$. Then…
View solution →Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given…
View solution →A coin is tossed three times. Let $X$ denote the number of times a tail follows a head. If $\mu$ and $\sigma^2$ denote the mean and variance of $X$, then the value of…
View solution →If $A$ and $B$ are two events such that $P(A \cap B)=0.1$, and $P(A \mid B)$ and $P(B \mid A)$ are the roots of the equation $12 x^2-7 x+1=0$, then the value of $\frac{P(\bar{A}…
View solution →$A$ and $B$ alternately throw a pair of dice. A wins if he throws a sum of 5 before $B$ throws a sum of 8 , and $B$ wins if he throws a sum of 8 before $A$ throws a sum of 5 . The…
View solution →Two number $\mathrm{k}_1$ and $\mathrm{k}_2$ are randomly chosen from the set of natural numbers. Then, the probability that the value of…
View solution →Bag $B_1$ contains 6 white and 4 blue balls, Bag $B_2$ contains 4 white and 6 blue balls, and Bag $B_3$ contains 5 white and 5 blue balls. One of the bags is selected at random…
View solution →Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then…
View solution →$$ \text { Given three indentical bags each containing } 10 \text { balls, whose colours are as follows : } $$ $$ \begin{array}{lccc} & \text { Red } & \text { Blue } & \text {…
View solution →If the probability that the random variable $X$ takes the value $x$ is given by $P(X=x)=k(x+1) 3^{-x}, x=0,1,2,3 \ldots$, where $k$ is a constant, then $P(X \geq 3)$ is equal to
View solution →A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let $X$ denote the number of defective pens. Then the variance of $X$ is
View solution →The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is
View solution →Let a random variable X take values 0, 1, 2, 3 with P(X=0)=P(X=1)=p, P(X=2)=P(X=3) and E(X2)=2E(X). Then the value of 8p−1 is :
View solution →If A and B are two events such that $P(A) = 0.7$, $P(B) = 0.4$ and $P(A \cap \overline{B}) = 0.5$, where $\overline{B}$ denotes the complement of B, then $P\left(B \mid (A \cup…
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