A statistics professor has two students helping her with her research. The proba

Question

A statistics professor has two students helping her with her research. The probability that the undergraduate student will successfully finalize the research project is 0.92: the probability that the graduate student will successfully finalize the research project is 0.95: the probability that at least one of the two students will successfully finalize the research project is 0.98. Find the probabilities that (a) neither of them will finalize the project: (b) at least one of the students will not finalize the project: (c) exactly one of the students will not finalize the project.

Explanation / Answer

We are given,

P (undergraduate student successfully finalize) = 0.92

P (graduate student successfully finalize) = 0.95

P (undergraduate student successfully finalize or graduate student successfully finalize) = 0.98

Question a)

P (neither) = 1 – 0.98 = 0.02

Answer: The probability that neither will finalize the report is 0.02

Question b)

P (undergraduate student will not successfully finalize) = 1- 0.92 = 0.08

P (graduate student will not successfully finalize) = 1 -0.95 = 0.05

P (at least) = 0.08 + 0.05 – 0.02 = 0.11

Answer: The probability that at least one of the students will not finalize the project is 0.11

Question c)

P (exactly one) = (0.08 -0.02) + (0.05-0.02) = 0.06 + 0.03 = 0.09

Answer: The probability that exactly one of the students will not finalize the project is 0.09

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