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02 Jan 2018, 01:12
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C
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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
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
02 Jan 2018, 04:23
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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
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
04 Jan 2018, 01:27
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=>
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
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
