PROBABILITY 1

A number is chosen at random from 1 – 15 inclusive. Find the probability that it is a multiple of five or an even number greater than 8.

Solution

THIS IS A NON-MUTUALLY EXCLUSIVE EVENT.

Let n(S) represent sample space

P(E) = probability of even number greater than 8

P(M) = probability of a multiple of 5

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

n(E) = {10, 12, 14} = 3

n(M) = {5, 10, 15} = 3

But 10 appears on both categories.

P(E) = ³/15

P(M) = ³/15

P(EnM) = ¹/15

………………………….

P(EuM) = P(E) + P(M) - P(EnM)  

P(EuM) = ³/15 + ³/15 -¹/15

              = ⁵/15

              = ¹/3  after simplification

∴ P(EuM) = ¹/5

TRY THIS………………

A number is chosen at random from 17 – 30 inclusive. Find the probability that it is a multiple of 5 or an even number.