You are given that A and B are two events such that P(B 35 P(A, B 45 then P(A equals)))

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Text Solution

`3/10``1/5``1/2``3/5`

Solution : Here,P(B)=`3/5`,P(A/B)=1/2and P(`AcupB`)=4/5 <br> `becauseP(A//B)=(P(AcapB))/(P(B))` <br> `rArr1/2=(P(AcapB))/(3//5)` <br> `rArrP(AcapB)=3/5xx1/2=3/10` <br> and `P(AcupB)=P(A)+P(B)-P(AcapB)` <br> `rArr4/5=P(A)+3/5-3/10` <br> `thereforeP(A)=4/5-3/5+3/10=(8-6+3)/10=1/2`

If A and B are two events such that P(B) = `3/5`, P(A|B) = `1/2` and P(A ∪ B) = `4/5`, then P(A) equals `1/2`.

Explanation:

Given that: P(B) = `3/5`, P(A|B) = `1/2` and P(A ∪ B) = `4/5`

We know that P(A|B) = `("P"("A" ∩ "B"))/("P"("B"))`

⇒ `1/2 = ("P"("A" ∩ "B"))/(3/5)`

∴ P(A ∩ B) = `3/10`

Now  P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

`4/5 = "P"("A") + 3/5 - 3/10`

⇒ P(A) = `4/5 - 3/5 + 3/10`

= `1/5 + 3/10`

= `5/10`

= `1/2`