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Question
Evaluate P(A ∪ B), if 2P(A) = P(B) = `5/13` and P(A | B) = `2/5`
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Solution
It is given that,
2P(A) = P(B) = `5/13`
`\implies` P(A) = `5/26` and P(B) = `5/13`
`\implies` P(A | B) = `2/5`
`\implies (P(A ∩ B))/(P(B)) = 2/5`
`\implies P(A ∩ B) = 2/5 xx P(B)`
= `2/5 xx 5/13`
= `2/13`
It is known that,
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
`\implies` P(A ∪ B) = `5/26 + 5/13 - 2/13`
`\implies` P(A ∪ B) = `(5 + 10 - 4)/26`
`\implies` P(A ∪ B) = `11/26`
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