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
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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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.BTGmoderatorDC wrote: ↑Wed Apr 01, 2020 5:15 pmIf 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
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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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:BTGmoderatorDC wrote: ↑Wed Apr 01, 2020 5:15 pmIf 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
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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