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26 May 2021, 06:45
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C
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The probability of rain showers in Barcelona on any given day is 0.4. What is the probability that it will rain on exactly one out of three straight days in Barcelona?
A. 0.144
B. 0.072
C. 0.432
D. 0.72
E. 0.288
A. 0.144
B. 0.072
C. 0.432
D. 0.72
E. 0.288
Updated on: 17 Feb 2022, 08:03
Originally posted by BrentGMATPrepNow on 26 May 2021, 06:55.
Last edited by BrentGMATPrepNow on 17 Feb 2022, 08:03, edited 1 time in total.
Last edited by BrentGMATPrepNow on 17 Feb 2022, 08:03, edited 1 time in total.
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Bunuel
The probability of rain showers in Barcelona on any given day is 0.4. What is the probability that it will rain on exactly one out of three straight days in Barcelona?
A. 0.144
B. 0.072
C. 0.432
D. 0.72
E. 0.288
A. 0.144
B. 0.072
C. 0.432
D. 0.72
E. 0.288
Key concept: P(Event A happening) = 1 - P(Event A not happening)
If P(rain) = 0.4, then P(no rain) = 1 - 0.4 = 0.6
P(rain exactly once) = P(rain day 1 AND no rain day 2 AND no rain day 3 OR no rain day 1 AND rain day 2 AND no rain day 3 OR no rain day 1 AND no rain day 2 AND rain day 3)
= (0.4 x 0.6 x 0.6) + (0.6 x 0.4 x 0.6) + (0.6 x 0.6 x 0.4)
= 0.144 + 0.144 + 0.144
= 0.432
Answer: C
General Discussion
26 May 2021, 07:30
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Chance of rain: 40/100
Chance of no rain: 60/100
Chance of rain on one day: 40/100 * 60/100 * 60/100
= 4*6*6/1000
= 144/1000 This however is the probability that it will rain only on the first day and not the next 2.
Now multiply that by 3 to get the chance that it will rain on exactly one of the 3 days:
144/1000 * 3
432/1000
0.432
Answer C
Chance of no rain: 60/100
Chance of rain on one day: 40/100 * 60/100 * 60/100
= 4*6*6/1000
= 144/1000 This however is the probability that it will rain only on the first day and not the next 2.
Now multiply that by 3 to get the chance that it will rain on exactly one of the 3 days:
144/1000 * 3
432/1000
0.432
Answer C
