The student council for a school of science and math has one

The student council for a school of science and math has one representative from each of the five academic departments: biology (B), chemistry (C), mathematics (M), physics (P), and statistics (S). Two of these students are to be randomly selected for inclusion on a university-wide student committee (by placing five slips of paper in a bowl, mixing, and drawing out two of them).

(a) What are the 10 possible outcomes (simple events)?

{ (B, C), (B, M), (B, P), (B, S), (C, M), (C, P), (C, S), (M, P), (M, S) }{ (B, C), (B, M), (B, P), (B, B), (C, M), (C, P), (C, C), (M, P), (M, S), (P, S) }     { (B, C), (B, M), (B, P), (B, S), (C, M), (C, P), (C, S), (M, P), (M, S), (P, S) }{ (B, C), (B, M), (P, P), (B, S), (C, M), (C, P), (C, S), (M, P), (M, S), (P, S) }{ (B, C), (B, M), (B, S), (C, M), (C, P), (C, S), (M, P), (M, S), (P, S) }

(b) From the description of the selection process, all outcomes are equally likely; what is the probability of each simple event?


(c) What is the probability that one of the committee members is the chemistry department representative?


(d) What is the probability that both committee members come from laboratory science departments?

Solution

(a) As this doesn\'t need to be an ordered duple, possible outcomes:

(B,C),(B,M),(B,P),(B,S),(C,M),(C,P),(C,S),(M,P),(M,S),(P,S)

(b) Probability of each simple event = 1/10 = 0.1

(c) Probability that one is a chemistry department representative = 4/10 = 0.4

(d) Proabability that coth come from laboratory science departments = 3/10 = 0.3