Question

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

• A. $\frac{8}{125}$
• B. $\frac{5}{16}$
• C. $\frac{8}{25}$
• D. $\frac{2}{25}$

Answer 1

The correct option is B $\frac{5}{16}$

Prob. that it rains on the 1st day $=\frac{1}{2}$
Prob. that it rains on the 2nd day $=\frac{1}{2}$
Prob. that it rains on the 3rd day $=\frac{1}{2}$
Prob. that it rains on the 4th day $=\frac{1}{2}$
probability that it rains on the 5th day $=\frac{1}{2}$
probability that it rains on any day in a 5-day period $=\frac{1}{32}$.
prob. that it rains on exactly 3 days in a 5-day period.
${=}^5{C}_3\times \frac{1}{32}{=}^5{C}_2\times \frac{1}{32}=\frac{10}{32}=\frac{5}{16}.$