Question

A two digit number is formed with digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is

1. an odd number?
2. a multiple of 5?

Answer 1

Sample Space (S) = {23, 25, 27, 29, 32, 35, 37, 39, 52, 53, 57, 59, 72, 73, 75, 79, 92, 93, 95, 97}

∴ n(S) = 20

Event A: The number is odd.

∴ A =  {23, 25, 27, 29, 35, 37, 39, 53, 57, 59, 73, 75, 79, 93, 95, 97}

∴ n(A) = 16 

∴ P(A) = `(n(A))/(n(S))`

= `16/20`

= `4/5`

Event B: The number is a multiple of 5.

B = {25, 35, 75, 95}

∴ n(B) = 4 

∴ P(B) = `(n(B))/(n(S))`

= `4/20`

= `1/5`