Probability and statistics

Question

A nursery advertises that it has 16 elm trees for sale. Unknown to the nursery, 5 of the trees have already been infected with Dutch elm disease and will die within a year. (Hint: The buying of trees is done without replacement)

a.) If a buyer purchases three trees, what is the probability that all three trees will be healthy?

b.) What is the probability that at least one of the trees is infected?

00.3125

0.0393

O.6875

0.2946

Answer 1

A nursery advertises that it has 16 elm trees for sale. Unknown to the nursery, 5 of the trees have already been infected with Dutch elm disease and will die within a year. (Hint: The buying of trees is done without replacement).

a.) If a buyer purchases three trees, what is the probability that all three trees will be healthy?

Answer:

Ways of picking 3 healthy trees out of 11 healthy trees = 11 Choose 3 = 165

Ways of picking 0 infected trees out of 5 infected tree = 5 Choose 0 = 1

Ways of picking 3 trees out of 16 trees = 16 Choose 3 = 560

Hence, probability of picking 3 healthy trees out of 16 = (11 Choose 3) * 5 Choose 0 / 16 Choose 3

= 165 * 1 / 560 = 0.2946

b.) What is the probability that at least one of the trees is infected?

Probability that at least one of the trees is infected = 1- 0.2946 = 0.7054