Question

Grafting, the uniting of the stem of one plant with the stem or root of another, is widely used commercially to grow the stem of one variety that produces fine fruit on the root system of another variety. Suppose grafts are done one at a time. Each graft is successful with probability 0.55, independently of each other. Given there were no failed grafts in the first seven done, what is the probability that there will be at least one failed graft in the next four? O 0.96 o none of the answers provided here O 0.91 0 0.87 O 0.99

Answer 1

P(successful graft) = 0.55

Since the outcomes are independent, the information regarding prior cases are irrelevant.

Therefore, P(there will be at least one failed graft in next four | no failed grafts in first seven) = P(there will be at least one failed graft in next four)

= 1 - P(all of the next 4 grafts will be successful)

= 1 - 0.55⁴

= 0.91