Question

In the fall, you go to the local nursery and purchase a package of 10 rose plants. The clerk informs you that on average you can expect 5% of the plants to not live through the winter. Assume that the plants are a random sample.
a) Use the binomial formula to determine the probability that one or more of the plants will not survive the winter.
b) What is the probability that all the plants will survive? Write how the binomial formula is used to calculate the probability.

Answer 1

Let success be that a plant dies in the winter and failure be that a plant survives the winter, then
 p = 0.05, q = 1 - 0.05 = 0.95

a.) P(1 or more will not survive the winter) = 1 - P(all will survive the winter) = 1 - P(0) = 1 - 10C0 (0.05)^0 (0.95)^10 = 1 - 1(1)(0.5987) = 0.4013

b.) P(all will survive) = P(none will die) = P(0) = 0.5987