If the probability of rain on any given day is 50%, what is

Hi All,

We're told that the probability of rain on any given day is 50%. We're asked for the probability that it will rain on AT LEAST three days in a ROW during a five-day period. This question can be approached in a number of different ways; you might find it easiest to do a little math and 'map out' the various possible ways to get at least 3 days of rain in a row.

Since there are two events (rain or no rain) that have an equal chance of occurring each day, with 5 days in a row, there are (2)(2)(2)(2)(2) = 32 possible outcomes for the 5 days. The number of outcomes that include AT LEAST 3 days of rain IN A ROW are....

3 days:
RRRNN
NRRRN
NNRRR

4 days:
RRRRN
RRRNR
RRNRR
RNRRR
NRRRR

5 days:
RRRRR

8 options out of 32 total = 8/32 = 1/4

Final Answer: B

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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 a row during a five-day period?

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

OA B

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