Question

Claims filed in a year by a policyholder have a POISSON DISTRIBUTION with Expected Value .40 The number of claims filed by different policyholders are independent If two policyholders are chosen randomly, what is the probability that at least one of them will file no claims?

Answer 1

0.938448064

Step-by-step explanation:

Using the formula for poisson distribution

We have the Poisson Formula as ;

P(x; μ) = (e-μ) (μx) / x!

Where our μ = 0.40

Substituting the value into the formula we have

[exp(−0.4)∗0.40]/0!+[exp(−0.4)∗0.41]/1!

={(0.67×1)/1 }+ (0.67×0.40)/1

=(0.67/1) + (0.268/1)

=0.67+ 0.268

=0.938448064