At a local college, 38% of students are enrolled in a statistics course and 52%

Question

At a local college, 38% of students are enrolled in a statistics course and 52% of students are enrolled in an accounting course. Also, 21% of students are enrolled in both statistics and accounting.

In blank #1 enter the probability that a randomly selected student is in statistics or accounting. In blank #2 enter the probability that a randomly selected student is in accounting, given that they are in statistics. In blank #3 enter the probability that a randomly selected accounting student is in statistics. In blank #4 enter the probability that a randomly selected student is not in either course. In blank #5 enter the probability that a randomly selected student is in accounting but not in statistics. Round your answer to 2 decimal places (including numbers like 0.20) and enter your answers as 0.24 and not .24.

Explanation / Answer

P(statistics course) = 0.38

P(accounting course) = 0.52

P(statistics and accounting) = 0.21

a) P(statistics or accounting) = P(statistics) + P(accounting) - P(statistics and accounting)

                                               = 0.38 + 0.52 - 0.21

                                               = 0.69

b) P(accounting | statistics) = P(accounting and statistics) / P(statistics)

                                            = 0.21 / 0.38

                                            = 0.55

c) P(statistics) = 0.38

d) P(not in either course) = 1 - P(statistics or accounting) = 1 - 0.69 = 0.31

e) P(accounting and not statistics) = P(accounting) - P(accounting and statistics) = 0.52 - 0.21 = 0.31

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