Question

An integer is choosen at random between 1 and 100.Find the probability that it is( 1). divisible by a 8. (2.) not divisible by 8.

Answer 1

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) = 12/98 = 6/49
P(divisible by 8) = 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 - 6/49 = (49 - 6)/49 = 43/49