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 the probability of getting an odd number for odd number of times is :
Solution
P(odd no. twice) = P(even no. thrice)<br><br>$$ \Rightarrow {}^n{C_2}{\left( {{1 \over 2}} \right)^n} = {}^n{C_3}{\left( {{1 \over 2}} \right)^n} \Rightarrow n = 5$$<br><br>Success is getting an odd number then P(odd successes) = P(1) + P(3) + P(5)<br><br>$$ = {}^5{C_1}{\left( {{1 \over 2}} \right)^5} + {}^5{C_3}{\left( {{1 \over 2}} \right)^5} + {}^5{C_5}{\left( {{1 \over 2}} \right)^5}$$<br><br>$= {{16} \over {{2^5}}} = {1 \over 2}$
About this question
Subject: Mathematics · Chapter: Probability · Topic: Classical and Axiomatic Probability
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