A college job placement center has requests from five students for employment interviews. Three of these
students are math majors, and the other two students are statistics majors. Unfortunately, the interviewer
has time to talk to only two of the students. These two will be randomly selected from among the five.
(a) What is the sample space for the chance experiment of selecting two students at random? (Hint: You
can think of the students as being labeled A, B, C, D, and E. One possible selection of two students is
A and B. There are nine other possible selections to
(b) Are the outcomes in the sample space equally likely?
(c) What is the probability that both selected students are statistics majors?
(d) What is the probability that both students are math majors?
(e) What is the probability that at least one of the students selected is a statistics major?
(f) What is the probability that the selected students have different majors?
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(a) The sample space for the chance experiment of selecting two students at random is {AB, AC, AD, AE, BC, BD, BE, CD, CE, DE}.
(b) Yes, the outcomes in the sample space are equally likely.
(c) There are 2 statistics majors out of the 5 students, so the probability of selecting a statistics major first is 2/5. After that, there is 1 statistics major left out of the remaining 4 students, so the probability of selecting a statistics major second is 1/4. The probability that both selected students are statistics majors is (2/5) * (1/4) = 1/10.
(d) There are 3 math majors out of the 5 students, so the probability of selecting a math major first is 3/5. After that, there is 2 math majors left out of the remaining 4 students, so the probability of selecting a math major second is 2/4. The probability that both selected students are math majors is (3/5) * (2/4) = 3/10.
(e) The probability that at least one of the students selected is a statistics major can be found by subtracting the probability that both selected students are math majors from 1. So, the probability is 1 - 3/10 = 7/10.
(f) To find the probability that the selected students have different majors, we can subtract the probability that both selected students have the same major from 1. The only ways for both selected students to have the same major is if both are statistics majors or both are math majors. We already calculated the probabilities for both of these cases, which are 1/10 for both statistics majors and 3/10 for both math majors. So, the probability that the selected students have different majors is 1 - (1/10 + 3/10) = 6/10 or 3/5.
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