Question

A number is selected at random from first 100 whole numbers. find the probability that the number is divisible by 8 or 12

Answer 1

Required probability = 4/25

STEP-BY-STEP EXPLANATION:

A number can be chosen at random from the first 100 whole numbers in 100 ways and this is the number of outcomes in the event space.

Let A be the event - 'the number selected is divisible by 8' and B be the event - 'the number selected is divisible by 12'.

Then AB is the event - 'the number selected is divisible by both 8 or 12, i.e., divisible by 24'.

Number of outcomes favourable to the event A is

n(A) = [ 100/8 ] = 12

Similarly n(B) = [ 100/12 ] = 8

and n(AB) = [ 100/24 ] = 4

Thus P(A) = 12/100, P(B) = 8/100 & P(AB) = 4/100

Required probability is = P(A + B)

= P(A) + P(B) - P(AB)

= 12/100 + 8/100 - 4/100

= 16/100 = 4/25

Answer 2

1. Step-by-step explanation:

A number is selected at random from first 100 whole numbers. Find the probability that the number is divisible by 8 or 12.