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Question

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


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 $$8$$ , $$P(E) =\dfrac{ n(E)}{n(S)} = \dfrac{12}{98} = \dfrac{6}{49}$$.
$$P($$ divisible by $$8) = \dfrac{6}{49}$$.
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 $$8) = 1 - \dfrac{6}{49} = \dfrac{(49 - 6)}{49} =\dfrac{ 43}{49}$$.

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