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?

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, λ ) = 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 ...