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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.
Solution
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`
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