Sum

Solve the following:

Let A and B be independent events with P(A) = `1/4`, and P(A ∪ B) = 2P(B) – P(A). Find `"P"("B'"/"A")`

Advertisement Remove all ads

#### Solution

A and B are independent events.

∴ P(A ∩ B) = P(A) × P(B)

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

∴ P(A ∪ B) = P(A) + P(B) – P(A) × P(B)

∴ 2P(B) – P(A) = P(A) + P(B) – P(A) × P(B) ...[∵ P(A ∪ B) = 2P(B) – P(A)]

∴ `2"P"("B") - 1/4 = 1/4 + "P"("B") - 1/4 xx "P"("B")`

∴ `2"P"("B") - "P"("B") + 1/4 "P"("B") = 1/4 + 1/4`

∴ `5/4 "P"("B") = 2/4`

∴ P(B) = `2/5`

`"P"("B'"/"A") = ("P"("B'" ∩ "A"))/("P"("A"))`

= `("P"("B'") xx "P"("A"))/("P"("A"))`

= P(B')

= 1 – P(B)

= `1 - 2/5`

= `3/5`

Concept: Independent Events

Is there an error in this question or solution?

Advertisement Remove all ads

#### APPEARS IN

Advertisement Remove all ads

Advertisement Remove all ads