PROBABILITY 7

A number is chosen at random from 1 – 15 inclusive. Find the probability that it is a multiple of three 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 3

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) = {3, 6, 9,12,15} = 5

But 6 and 12 appears on both categories.

P(E) = ⁷/15

P(M) = ⁵/15

P(EnM) = ²/15

………………………….

P(EuM) = P(E) + P(M) - P(EnM)  

P(EuM) = ⁷/15 + ⁵/15 -²/15

              = ¹⁰/15

              = ²/5

∴ P(EuM) = ²/5

TRY THIS………………

A number is chosen at random from 7 – 26 inclusive. Find the probability that it is a multiple of 3 or an even number.