Question

Let x represent the number of times a cat attempts to catch the nest of a bird in the wilderness in a given day. x is poisson distributed with expected value 5. consider 6 randomly chosen cats in the area. what is the exact probability that the total number of attempts of all 6 cats in a day is less than 3?

Answer 1

Given Poisson distribution, with E[x]=5.

For one cat
P(X<3)
=P(X=0)+P(X=1)+P(x=2)
=0.006738+0.033690+0.084224
=0.124652
Using tables, or according to formula
P(x, &lambda; ) = lambda^(x)e^(-lambda)/x!

Assuming random and independent choice of cats, by the multiplication rule,
Probability that all six cats will attempt less than three times
=(0.124652019)^6
=0.00000375142193....