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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