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The probability that an afternoon storm will occur on Monday is 40%, t

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The probability that an afternoon storm will occur on Monday is 40%, t  [#permalink]

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New post 02 Jan 2018, 01:12
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

68% (02:24) correct 32% (02:20) wrong based on 56 sessions

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[GMAT math practice question]

The probability that an afternoon storm will occur on Monday is 40%, the probability that an afternoon storm will occur on Tuesday is 50%, and the probability that an afternoon storm will occur on Wednesday is 40%. What is the probability that afternoon storms will occur on exactly two of these three days?

A. 0.28
B. 0.30
C. 0.32
D. 0.34
E. 0.36

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Re: The probability that an afternoon storm will occur on Monday is 40%, t  [#permalink]

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New post 02 Jan 2018, 04:23
1
1
P(M) = 0.4 , P(not M) = 0.6
P(T) = 0.5 , P(not T) = 0.5
P(W) = 0.4 , P(not W) = 0.6

The probability that afternoon storms will occur on exactly two of these three days

P = P(M).P(T).(not W)+P(M).P(not T).P(W)+ P(not M).P(T).P(W)

= 0.4*0.5*0.6+0.4*0.5*0.4+0.6*0.5*0.4

=0.32

Ans. C
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Re: The probability that an afternoon storm will occur on Monday is 40%, t  [#permalink]

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New post 04 Jan 2018, 01:27
=>

There are three cases to consider.

Case 1: Afternoon storms occur on Monday and Tuesday, but not on Wednesday.
Probability = 0.4 * 0.5 * 0.6 = 0.12

Case 2: Afternoon storms occur on Monday and Wednesday, but not on Tuesday.
Probability = 0.4 * 0.5 * 0.4 = 0.08

Case 3: Afternoon storms occur on Tuesday and Wednesday, but not on Monday.
Probability = 0.6 * 0.5 * 0.4 = 0.12

The probability that one of these three cases will occur is 0.12 + 0.08 + 0.12 = 0.32

Therefore, the answer is C.

Answer: C
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Re: The probability that an afternoon storm will occur on Monday is 40%, t   [#permalink] 04 Jan 2018, 01:27
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