Given two events A and B. If odds against A are as 2:1 and those in favour of A∪B are as 3:1, then
A
16≤P(B)≤34
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B
512≤P(B)≤34
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C
14≤P(B)≤35
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D
18≤P(B)≤34
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Solution
The correct option is B512≤P(B)≤34 Odds against A=21⇒P(A)=13
Also, odds in favour of A∪B=31⇒P(A∪B)=34
Now, P(A∪B)=P(A)+P(B)−P(A∩B)≤P(A)+P(B) ⇒34≤13+P(B) ⇒512≤P(B)
We have B⊆A∪B ∴P(B)≤P(A∪B)=34
Hence, 512≤P(B)≤34