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Question
If A and B are two events such that `P(A/B) = 2 xx P(B/A)` and P(A) + P(B) = `2/3`, then P(B) is equal to ______.
Options
`2/9`
`7/9`
`4/9`
`5/9`
Solution
If A and B are two events such that `P(A/B) = 2 xx P(B/A)` and P(A) + P(B) = `2/3`, then P(B) is equal to `underlinebb(2/9)`.
Explanation:
Given,
`P(A/B) = 2 xx P(B/A)`
`\implies (P(A ∩ B))/(P(B)) = 2 xx (P(A ∩ B))/(P(A))`
`\implies` P(A) = 2P(B) ...(i)
Now, P(A) + P(B) = `2/3`
From (i),
2P(B) + P(B) = `2/3`
`\implies` P(B) = `2/9`.
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