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प्रश्न
For any two events A and B, if `P(barA) = 1/2, P(barB) = 2/3 "and" P(A\capB) = 1/4, "then" P(barA//barB)` equals ______.
पर्याय
`3/8`
`8/9`
`5/8`
`1/4`
MCQ
रिकाम्या जागा भरा
उत्तर
For any two events A and B, if `P(barA) = 1/2, P(barB) = 2/3 "and" P(A\capB) = 1/4, "then" P(barA//barB)` equals `5/8`.
Explanation:
`P(barA) = 1/2, P(barB) = 2/3` and `P(A\capB) = 1/4`
⇒ `P(A) = 1/2; P(B) = 1/3`
We have, `P(A\cupB) = P(A) + P(B) - P(A\capB)`
= `1/2 + 1/3 - 1/4`
= `7/12`
`P(barA/barB) = (P(barA\capbarB))/(P(barB))`
= `(P(bar(A\cupB)))/(P(barB))`
= `(1 - P(A\cupB))/(P(barB))`
= `(1 - 7/12)/(2/3)`
= `5/8`
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