If the probability of rain on any given day in City Dhaka is 50 percent, what is the probability that it rains on exactly 2 days in a 4-day period?

Question: If the probability of rain on any given day in City Dhaka is 50 percent, what is the probability that it rains on exactly 2 days in a 4-day period?

Solution:
If the probability of rain on any given day in City Dhaka is 50 percent
the probability of rain on any given day = 1/2
the probability of no rain on any given day = 1/2

selecting 2 days out of 4 = ⁴C₂

∴the probability that it rains on exactly 2 days in a 4-day period is = ⁴C₂ × 1/2 × 1/2 × 1/2 × 1/2
= 6 × 1/2⁴
= 6 × 1/16
= 3/8