The probability that a person living in a certain city owns a dog is estimated to be 0.3. Find the probability that the tenth person randomly interviewed in that city is the fifth one to own a dog.

the probability is 0.051 (5.1%)

Step-by-step explanation:

since the fact that person owns a dog independently of the behaviour of the other people , then the random variable X= number of people that owns a dog from 10 interviewed , follows a binomial distribution .

P(X=x) = C (n,x)* p^x * (1-p)^(n-x)

where

n= sample size = 10

p= probability that a person owns a dog = 0.3

x= number of people found that owns a dog = 5

C(n,x) = combinations of 5 persons who owns a dog from 10 interviewed ( number of times we can observe 5 people from 10 owning a dog)

for our case we know that the tenth person has a dog , then considering that constraint  the number of times observed must be modified  and is equal to the number of times we can observe 4 people out of 9 that has a dog ( since we know already that the tenth will be a person who owns a dog)

therefore

P(tenth person is the fifth one to own a dog) = C (n-1,x-1)* p^x * (1-p)^(n-x)

= C (9,4)* 0.3^5 * 0.7^(10-5) = 0.051 (5.1%)

therefore the probability is 0.051 (5.1%)

can i get the link to the assignment?

step-by-step explanation: