Question

In a political science class there are 15 political science majors and 9 non-political science majors. 4 students are randomly selected to present a topic. What is the probability that at least 2 of the 4 students selected are political science majors? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Total students = 15 + 9 = 24

Total number of ways to select 4 students out of 24 = 24C4 = 24! / (4! * (24 - 4)!) = 10626

P(at least 2 of the 4 students are political science majors) = P(2 out of the 4 students are political science majors) + P(3 out of the 4 students are political science majors) + P(4 out of the 4 students are political science majors)

                                                               = (15C2 * 9C2 / 10626) + (15C3 * 9C1 / 10626) + (15C4 / 10626)

                                                               = (105 * 36 / 10626) + (455 * 9 / 10626) + (1365 / 10626)

                                                               = 0.8696