3 At a particular factory the acciden averaging 3 fires per

3. At a particular factory the acciden averaging 3 fires per two months. a particular factory the accidents occur according, to Poisson law a). What is the probability that there 3 or more accidents in the next. 3 months? b). What is the probability that there are no accidents for the next 5 months

Solution

The accidents occur according to Poisson law averaging 3 fires per two months,i.e 1.5 fires per month.

Let X be a random variable denoting the accidents that will occur in the next 3 months.

X~Poisson(4.5)

a) The probability that there 3 or more accidents in the next 3 months=P(X>=3)=1-P(X<=2)=1-0.173578=0.826422

b)Let Y be a random variable denoting the accidents that will occur in the next 5 months.

Y~Poisson(7.5)

The probability that there are no accidents for the next 5 months=P(Y=0)=0.0005531