PROBABILITY 12

A number is chosen at random from 1 – 15 inclusive. Find the probability that it is a multiple of seven or an even number.

Solution

THIS IS A NON-MUTUALLY EXCLUSIVE EVENT.

Let n(S) represent sample space

P(E) = probability of even number

P(M) = probability of a multiple of 7

n(S) = {1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11, 12, 13, 14, 15} = 15

n(E) = {2, 4, 6, 8, 10, 12, 14} = 7

n(M) = {7, 14 } = 2

But 14 appears on both categories.

P(E) = ⁷/15

P(M) = ²/15

P(EnM) = ¹/15

………………………….

P(EuM) = P(E) + P(M) - P(EnM) 

P(EuM) = ⁷/15 + ²/15 -¹/15

              = ⁸/15

              = ⁸/15

∴ P(EuM) = ⁸/15

TRY THIS………………

A number is chosen at random from 4 – 30 inclusive. Find the probability that it is a multiple of 3 or an even number.