# Solve the following: Let A and B be independent events with P(A) = 14, and P(A ∪ B) = 2P(B) – P(A). Find P(B'A) - Mathematics and Statistics

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")

#### 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?

#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 9 Probability
Miscellaneous Exercise 9 | Q II. (12) (c) | Page 214