Question

A seedling supplier sells equal proportions of pine and fir seedlings (50% each). Based on historical evidence, the following probabilities pertaining to the mortality rates of seedlings are also known:
P (seedling will not survive) = 0.0f)

P (seedling is a pine AND it will not survive) = 0.03
a) If seedlings are sold in packages of 20, what is the probability that a sample of three (3) taken without replacement contains at least one (1) seedling that will not survive? Hint: the number of items labeled a success is the expected number of seedlings that will not survive in a package of 20.

b) If a dead seedling has been found, what is the probability that it was a fir?

Answer 1

According to the question,

a) P(atleast one out of 3 seedling wont survive)

= 1 - P(all 3 seedling will survive) => A

P(seedling will not survive) = 0.05

P(seedling will survive) = 1 - 0.05 = 0.95

P(all 3 seedling will survive) = 0.953 = 0.85

Thus, from A

P(atleast one out of 3 seedling wont survive) = 1 - 0.85 = 0.15

b)

P(seedling will not survive) = 0.05

P(seedling is pine and seedling will not survive) = 0.03

Thus, P(seedling is fir and seedling will not survive) = 0.05-0.03 = 0.02

P(seedling is fir/ seedling is dead) = P(seedling is fir and seedling will not survive) / P(seedling will not survive)

= 0.02 / 0.05 = 0.40