Question

P. T. Barnum is famous for (supposedly) saying that "there's a sucker" -that is, a fool - "born every minute." Suppose that our latest research indicates that today there are an expected 3.2 suckers born every minute! Suppose each arrival of a sucker is an independent event so that the mean rate of suckers being born is a constant 3.2 per minute, regardless of how many suckers arrived in any other minute. What is the probability that there will be exactly 4 suckers born in the next minute? Use four decimal places.

Answer 1

latest research indicates that today there are an expected 3.2 suckers born every minute

Average number suckers born every minute : = 3.2

X : Number of  suckers born in the next minute

X follows Poisson distribution with = 3.2

Probability mass function of X given,

Probability that 'x' suckers born in the next minute is given by

probability that there will be exactly 4 suckers born in the next minute = P(X=4)

probability that there will be exactly 4 suckers born in the next minute = 0.1781