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Question

An integer is chosen at random between 1 and 100. The probability that it is divisible by 8 is m25. Find m

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Solution

Number of integers between 1 and 100 are 100.
Clearly, this is the size of the sample space also.
The first integer between 1 and 100 divisible by 8 is 8 and the last integer in the same range divisible by 8 is 96.
So, these numbers form an A.P. with first term 8 and common difference 8.
So, we have an=96, a1=d=8n1=ana1d=9688=11n=11+1=12.
So there are 12 integers between 1 and 100 that are divisible by 8 and each number is equally likely of being picked.
So the probability that a randomly chosen integer in the given range is divisible by 8 is 12100=325.

hence m=3

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