Question

An integer is chosen at random between 1 to 100 .find the probability that it is:(i) divisible by 8 (i)not divisible by 8.

Answer 1

Number of integer between 1 and 100 is 100 [ because question said an integer is chosen at random . If question says , an integer is chosen between 1 and 100 then you should exclude 1 and 100 then number of outcomes = 98 ]
So, you can say total number of sample space , n(S) = 100

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) = 12/100 = 3/25
P(divisible by 8) = 3/25

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 - 3/25 = 22/25