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 $9 p$ is equal to :
Solution
<p>Among the 5 digit numbers,</p>
<p>First number divisible by 7 is 10003 and last is 99995.</p>
<p>$\Rightarrow$ Number of numbers divisible by 7.</p>
<p>$= {{99995 - 10003} \over 7} + 1$</p>
<p>$= 12857$</p>
<p>First number divisible by 35 is 10010 and last is 99995.</p>
<p>$\Rightarrow$ Number of numbers divisible by 35</p>
<p>$= {{99995 - 10010} \over {35}} + 1$</p>
<p>$= 2572$</p>
<p>Hence number of number divisible by 7 but not by 5</p>
<p>$= 12857 - 2572$</p>
<p>$= 10285$</p>
<p>$9P. = {{10285} \over {90000}} \times 9$</p>
<p>$= 1.0285$</p>
About this question
Subject: Mathematics · Chapter: Probability · Topic: Classical and Axiomatic Probability
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