Answer:
The probability is 0.2650
Step-by-step explanation:
Let's start assuming that men and women come in at the same rate.
Let's define the following random variables :
X : ''Number of people that enter a drugstore''
M : ''Number of men that enter a drugstore''
W : ''Number of women that enter a drugstore''
The number of people will be the number of men plus the number of women
⇒
X = M + W
We are also assuming that M and W are independent random variables.
X ~ Po (10)
M ~ Po (λ1)
W ~ Po (λ2)
λ1 = λ2 because we assumed that men and women come in at the same rate.
λ1 = λ2 = λ
λ1 + λ2 = λ + λ ⇒ 2λ = 10 ⇒ λ = 5
M ~ Po (5)
W ~ Po (5)
Because X is the sum of two independent Poisson random variables.
We are looking for :
Because we assume independence.
because is a Poisson random variable with λ = 5
