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Probability Problem - Cumbersome Solution

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by Scott@TargetTestPrep » Sun Dec 03, 2017 5:52 pm
student22 wrote:

Code: Select all

If the probability of rain on any given day in City X is 50 percent, what is the probability that it rains on exactly 3 days in a 5 day period?

A. 8/125

B. 2/25

C. 5/16

D. 8/25

E. 3/4
We can let R = rain and N = no rain, thus:

P(R - R - R - N - N) = (1/2)^5 = 1/32

Since R - R - R - N - N can be arranged in 5!/(3! x 2!) = 10 ways, the overall probability is 10 x 1/32 = 10/32 = 5/16.

Answer: C

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by Matt@VeritasPrep » Mon Dec 04, 2017 6:13 pm
Another approach:

Since p(R) = p(N), we can say:

p(0 days of R) = p(5 days of R)
p(1 day of R) = p(4 days of R)
p(2 days of R) = p(3 days of R)

and we know those six scenarios sum to 1.

p(0 days of R) is easy = (1/2)�
p(1 day of R) is similar = (1/2)� * 5

so our sum becomes

1/32 + 5/32 + p(2 days of R) + p(3 days of R) + 5/32 + 1/32 = 1

or

p(2 days of R) + p(3 days of R) = 20/32

or

2 * p(3 days of R) = 20/32

or

p(3 days of R) = 20/64 = 10/32 = 5/16
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by Scott@TargetTestPrep » Thu Oct 03, 2019 11:08 am
student22 wrote:

Code: Select all

If the probability of rain on any given day in City X is 50 percent, what is the probability that it rains on exactly 3 days in a 5 day period?

A. 8/125

B. 2/25

C. 5/16

D. 8/25

E. 3/4
P(RRRNN) = (1/2)^5 =1/32

Since RRRNN can be arranged in 5!/(3! x 2!) = 5 x 2 = 10 ways, the overall probability is 10/32 = 5/16.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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