Question

Suppose on an average $5$ out of $2000$ houses get damaged due to fire accident during summer. Out of $10,000$ houses in a locality, the probability that exactly $10$ houses will get damaged during summer is

• A. $\frac{e^{-5}{5}^{10}}{10!}$
• B. $\frac{e^{-10}{10}^{10}}{10!}$
• C. $\frac{e^{-25}{25}^{10}}{10!}$
• D. $\frac{e^{-15}{15}^{10}}{10!}$

Answer 1

The correct option is C $\frac{e^{-25}{25}^{10}}{10!}$

Here P.D parameter $\lambda =\frac{5}{2000}\times 10000=25$
Hence probability that exactly 10 houses will get damaged $=P(X=10)=\frac{e^{-25}(25{)}^{10}}{10!}$