Question

In a race, the probabilities of A and B winning the race are `1/3` and `1/6` respectively. Find the probability of neither of them winning the race.

Answer 1

Let A win the race be E₁

B wins the race be E₂

`P(E_1) = 1/3`, `P(E_2) = 1/6`

`P(E_1^' ∩ E_2^') = P(E_1^').P(E_2^')`

`= [1-P(E_+1)][1-P(E_2)]`

`= (1-1/3) (1-1/6)`

`= 2/3 xx 5/6 = 5/9`