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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # Let A, B, C, and D be events for which P(AorB)=0.6, P(A)=0.2  Question banks Downloads My Bookmarks Reviews Important topics
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Let A, B, C, and D be events for which P(AorB)=0.6, P(A)=0.2 [#permalink]
Expert's post
Let A, B, C, and D be events for which P(A or B) = 0.6, P(A) = 0.2, P(C or D) = 0.6, P(C) = 0.5

The events A and B are mutually exclusive, and the events C and D are independent.

(a) Find P(B)

(b) Find P(D)

[Reveal] Spoiler: OA
(a) 0.4 (b) 0.2

Math Review
Question: 14
Page: 298
Difficulty: medium

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GRE Instructor Joined: 10 Apr 2015
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Re: Let A, B, C, and D be events for which P(AorB)=0.6, P(A)=0.2 [#permalink]
Expert's post
Carcass wrote:
Let A, B, C, and D be events for which P(A or B) = 0.6, P(A) = 0.2, P(C or D) = 0.6, P(C) = 0.5

The events A and B are mutually exclusive, and the events C and D are independent.

(a) Find P(B)

(b) Find P(D)

[Reveal] Spoiler: OA
(a) 0.4 (b) 0.2

Math Review
Question: 14
Page: 298
Difficulty: medium

Key concepts:

- P(X or Y) = P(X) + P(Y) - P(X and Y)

- If X and Y are mutually exclusive events, then P(X and Y) = 0

- If X and Y are independent events, then P(X and Y) = P(X) * P(Y)

(a) Find P(B)
Since events A and B are mutually exclusive, we know that P(A and B) = 0
Take: P(A or B) = P(A) + P(B) - P(A and B) and replace parts with their given values.
We get: 0.6 = 0.2 + P(B) - 0
Solve to get: P(B) = 0.4

------------------------------------------------
(b) Find P(D)
Since events C and D are mutually exclusive, we know that P(C and D) = P(C) x P(D)
Take: P(C or D) = P(C) + P(D) - P(C and D) and replace parts with their given values.
We get: 0.6 = 0.5 + P(D) - [0.5 x P(D)]
Subtract 0.5 from both sides to get: 0.1 = P(D) - [0.5 x P(D)]
Factor out P(D) to get: 0.1 = P(D)[1 - 0.5]
Simplify to get: 0.1 = P(D)[0.5]

Divide both sides by 0.5 to get: P(D) = 0.1/0.5 = 1/5 = 0.2

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.  Re: Let A, B, C, and D be events for which P(AorB)=0.6, P(A)=0.2   [#permalink] 31 May 2019, 09:09
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