Question

Jason has not been studying and believes that the probability that he will pass his chemistry exam is 0.4, the probability that he will pass the biology exam is 0.3 and the probability that he will pass both exams is 0.18.

1) Find the probability that Jason will pass at least one of the exams.

2)Find the probability that he will pass the chemistry exam given that he passes the biology exam.

3)Find the probability that he will pass the biology exam if he passes the chemistry exam.

4)Find the probability that he will fail both exams.

Please answer questions and explain answer!! Thank you

Answer 1

1) P(pass at least one exam) = P(pass chemistry) + P(pass biology) - P(pass both)

                                               = 0.4 + 0.3 - 0.18

                                               = 0.52

2) P(pass chemistry | pass biology) = P(pass chemistry and pass biology) / P(pass biology) = 0.18 / 0.3 = 0.6

3) P(pass biology | pass chemistry) = P(pass chemistry and pass biology) / P(pass chemistry) = 0.18 / 0.4 = 0.45

4) P(fail both exams) = 1 - P(pass at least one exam) = 1 - 0.52 = 0.48