random Probability

Question

Fertile (female) cats produce an average of six litters per year. Suppose that one fertile, female cat is randomly chosen. In one year, find the probability she produces:

a. Find the probability that she has no litters in one year

b. Find the probability that she has at least two litters in a half year

c. Find the probability that she has exactly three litters in a half year

Answer 1

This is modelled by a Poisson Distribution, number of events over a fixed period of time.

Poisson probability is P(x;mu) = e^-mu * mu^x/x!, where x is actual number of events and mu is the average number of events over the period of time (6 for a year; 3 for a half year).

a. mu = 6 and x = 0

e^-6 * 6^0/0! = 0.003

b. mu = 3; determine and sum probabilities for x = 0 and 1, then subtract that probability from 1

we already know for x = 0, probability is 0.003

for x = 1

e^-6 * 6^1/1! = 0.015

total = 0.018

1 - 0.018 = 0.982

c. mu = 3 and x = 3

e^-6 * 6^3/3! = 0.089