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If the probability of rain on any given day in City X is 50%, 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
Please provide me the solution with the required steps.

The probability of it raining on any day is 1/2.

If it rains on exactly 3 out of the 5 days, then it does not rain on the other two days.

The probability it rains on exactly 3 days = probability of it raining for 3 days * probability of it not raining on the other 2 days * selecting 3 out of 5 days when it rains

= (1/2) ^3 * (1/2)^2 * 5C3 = (1/8 ) * (1/4) * 10 =10/32 = 5/16.