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Question

An integer is chosen at random between 1 and 100. Find the probability that it is: not divisible by 8.

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Solution

Number of integers between 1 and 100:2,3,4,5,.....99
so, sample space { or total outcomes } =98
So, you can say total number of sample space , n(S)=98
Now , numbers , which are divisible by 8 are : 8,16,24,32,40,48,56,64,72,80,88,96
So, total number which are divisible by 8=12
So, number of possible event , n(E)=12
Now, probability that it is divisible by 8 , P(E)=n(E)n(S)=1298=649.
P( divisible by 8)=649.
Probability that it is not divisible by 8 , P(E)=1 probability that is is divisible by 8,P(E).
E.g., P( not divisible by 8)=1649=(496)49=4349.

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