Question

If the probability of rain on any given day in Pune city is 50%, what is the probability that it rains on exactly 3 days In a 5-day period?

Answer 1

There are only 2 possibilities each day- raining & not raining.

As there is a span of 5 days, $n\left(S\right)=2^5=32$.

Now, we want probability of rain on exactly 3 days.

Ways of choosing 3 from 5 $={}^5{C}_3=n\left(A\right)=10$.

Then, Probability $=\frac{10}{32}=\frac{5}{16}$