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If the probability of rain on any given day is 50%, what is the probability that it will rain on at least three days in

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If the probability of rain on any given day is 50%, what is the probability that it will rain on at least three days in

by BTGmoderatorDC » Wed Apr 01, 2020 5:15 pm
If the probability of rain on any given day is 50%, what is the probability that it will rain on at least three days in a row during a five-day period?

A. 3/32
B. 1/4
C. 9/32
D. 5/16
E. 1/2


OA B

Source: Veritas Prep
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Re: If the probability of rain on any given day is 50%, what is the probability that it will rain on at least three days

by Jay@ManhattanReview » Wed Apr 01, 2020 11:09 pm
BTGmoderatorDC wrote: ↑
Wed Apr 01, 2020 5:15 pm
 If the probability of rain on any given day is 50%, what is the probability that it will rain on at least three days in a row during a five-day period?

A. 3/32
B. 1/4
C. 9/32
D. 5/16
E. 1/2

OA B

Source: Veritas Prep
Given that the probability of rain on any day = 50% = 1/2, there are 2 scenarios in a day: Rain OR No rain. So, for 5 days, there are 2*2*2*2*2 = 32 scenarios.

Rains on 3 days:
RRRNN
NRRRN
NNRRR

Total no. of ways = 3;

Rains on 4 days:
RRRRN
RRRNR
RNRRR
NRRRR

Total no. of ways = 4;

Rains on 5 days:
RRRRR

Total no. of ways = 1;

There are 3 + 4 + 1 = 8 scenarios out of 32 scenarios

So, the required probability = 8/32 = 1/4

The correct answer: B

Hope this helps!

-Jay
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Re: If the probability of rain on any given day is 50%, what is the probability that it will rain on at least three days

by Scott@TargetTestPrep » Fri Apr 03, 2020 7:45 am
BTGmoderatorDC wrote: ↑
Wed Apr 01, 2020 5:15 pm
 If the probability of rain on any given day is 50%, what is the probability that it will rain on at least three days in a row during a five-day period?

A. 3/32
B. 1/4
C. 9/32
D. 5/16
E. 1/2


OA B

Source: Veritas Prep
Let R = rain and N = no rain. To have rain on at least three days in a row during a five-day period, we could have:

RRRNN, NRRRN, NNRRR, RRRRN, NRRRR, RNRRR, RRRNR, or RRRRR.

Notice that the probability of R is ½ and the probability of N is also ½. Thus, the probability of any of the scenarios above is ½ x ½ x ½ x ½ x ½ = (½)^5 = 1/32. Since we have a total of 8 scenarios, the overall probability is 8 x 1/32 = 1/4.

Answer: B

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