Maharashtra State BoardHSC Science (General) 11th
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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")`

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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
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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
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