91Ó°ÊÓ

Given in the question that the probability there will be at least $2$such accidents in the next month . The monthly worldwide average number of airplane crashes of commercial airlines can be approximated by Poisson distribution as it is a rare event.

Given $\mathrm{λ}=3.5$

At least $2$accidents $⇒2$or more accidents

$⇒1-P[X≤1]$

$=1-\left[\frac{e^{-35}(3.5{)}^0}{0!}+\frac{(3.5{)}^1{e}^{-35}}{1!}\right]$

$=1-[0.0302+0.1057]$

We get,

$=0.864$

The probability that there will be at least $2$such accidents in the next month is$0.864$.

Given in the question that the probability that will be at most $1$accidents in the next month. The monthly worldwide average number of airplane crashes of commercial airlines can be approximated by Poisson distribution as it is a rare event.

Given$\mathrm{λ}=3.5$

At most 1 accident $=0$or $1$accident

$=P(X=0)+P(X=1)$

$={\mathrm{e}}^{-3.5}+3.5e^{-3.5}$

We get,

$=0.1359$

The probability that will be at most$1$accidents in the next month is$0.1359.$