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Question
The odds against a certain event are 5: 2 and odds in favour of another independent event are 6: 5. Find the chance that at least one of the events will happen.
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Solution
Let A and B be two independent events.
Odds against A are 5: 2
∴ The probability of occurrence of event A is given by
P(A) = `2/(5 + 2) = 2/7`
Odds in favour of B are 6: 5
∴ The probability of occurrence of event B is given by
P(B) = `6/(6 + 5) = 6/11`
∴ P(at least one event will happen)
= P(A ∪ B)
= P(A) + P(B) – P(A ∩ B)
= P(A) + P(B) – P(A) P(B) ...[∵ A and B are independent events]
= `2/7 + 6/11 - 2/7 xx 6/11`
= `2/7 + 6/11 - 12/77`
= `(22 + 42 - 12)/77`
= `52/77`
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