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The odds against a certain event are 5 t...

The odds against a certain event are 5 to 2, and the odds in favor of another event independent of the former are 6 to 5. Find the chance that one at least of the events will happen.

Text Solution

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Let `P(A)` is the probability of the first event and `P(B)` is the probability of the second event.
Then,`P(barA) = 5/7 and P(A) = 2/7`
`P(B) = 6/11 and P(barB) = 5/11`
Probability that at least one of the events will happen, `P(E) = P(AnnB) + P(barAnnB) +P(A+barB)`
As `A` and `B` are independent events, `P(AnnB) = P(A)*P(B)`.
`:. P(E) = 2/7*6/11+5/7*6/11+2/7*5/11`
`P(E) = 12/77+30/77+10/77 = 52/77`
So, required probability is `52/77`.
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