The probability that a man aged 35 years will die before reaching the age of 40 years may be taken as 0.018. Out of a group of 100 men, now aged 35 years, what is the approximate probability that one man will die within next five years?
(Given : \( e^{-1.8}=0.1653 \))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0.2975
The number of deaths X is binomial with n = 100 and p = 0.018. Since n is large and p is small, the Poisson approximation applies with
\( \displaystyle \lambda=np=100\times 0.018=1.8 \)
\( \displaystyle P(X=r)=\frac{e^{-\lambda}\lambda^r}{r!} \)
\( \displaystyle P(X=1)=\frac{e^{-1.8}\times 1.8}{1!} \)
\( \displaystyle =0.1653\times 1.8 \)
\( \displaystyle =0.29754\approx 0.2975 \)