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Question
If for two events A and B, P(A – B) = `1/5` and P(A) = `3/5`, then `P(B/A)` is equal to ______.
Options
`1/2`
`2/5`
`3/5`
`2/3`
Solution
If for two events A and B, P(A – B) = `1/5` and P(A) = `3/5`, then `P(B/A)` is equal to `underlinebb(2/3)`.
Explanation:
Given,
P(A – B) = `1/5` and P(A) = `3/5`
∵ P(A – B) = `P(A ∩ overlineB)`
= P(A) – P(A ∩ B)
`\implies 1/5 = 3/5 - P(A ∩ B)`
`\implies` P(A ∩ B) = `3/5 - 1/5 = 2/5`
Now `P(B/A) = (P(A ∩ B))/(P(A))`
= `(2/5)/(3/5)`
= `2/3`
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