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The probability of rain showers in Barcelona on any given day is 0.4.

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Bunuel
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The probability of rain showers in Barcelona on any given day is 0.4. [#permalink] New post   26 May 2021, 06:45
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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
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C
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BrentGMATPrepNow
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The probability of rain showers in Barcelona on any given day is 0.4. [#permalink] New post   Updated on: 17 Feb 2022, 08:03
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Bunuel wrote:
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



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

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.
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Re: The probability of rain showers in Barcelona on any given day is 0.4. [#permalink] New post   16 Feb 2022, 22:32
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Hi BrentGMATPrepNow, Slight calculation mistake in final answer
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Re: The probability of rain showers in Barcelona on any given day is 0.4. [#permalink] New post   17 Feb 2022, 08:04
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abybencent wrote:
Hi BrentGMATPrepNow, Slight calculation mistake in final answer


Pesky multiplication!!
Thanks for the heads up! I have edited my response accordingly.

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Re: The probability of rain showers in Barcelona on any given day is 0.4. [#permalink] New post   26 May 2021, 07:30
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
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Re: The probability of rain showers in Barcelona on any given day is 0.4. [#permalink] New post   06 Jun 2021, 02:42
P(rain) = 0.4 & P(no rain) = 1 - 0.4 = 0.6
p(exactly 1 day rain)=3* p( rain in 1 day and not in other 2 days)
=3*0.4*0.6*0.6
=0.432(Ans)

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Re: The probability of rain showers in Barcelona on any given day is 0.4. [#permalink]
06 Jun 2021, 02:42
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