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 a university-wide student committee. The two students will be selected by placing five slips of paper (numbered 1, 2, 3, 4, and 5) into a bowl, mixing, and drawing out two of them. (a) What are the 10 possible outcomes (simple events)? {(B, C), (B, M), (B, S), (C, M), (C, P), (C, S), (M, P), (M, S), (P, S)} {(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, S), (C, M), (C, P), (C, S), (M, P), (M, S), (P, 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), (P, P), (B, S), (C, M), (C, P), (C, S), (M, P), (M, S), (P, S)} (b) From the description of the selection process, all simple events are equally likely. What is the probability of each simple event? (c) What is the probability that one of the committee members is the statistics department representative? (d) What is the probability that both committee members come from laboratory science departments?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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 a university-wide student committee. The two students will be selected by placing five slips of paper (numbered 1, 2, 3, 4, and 5) into a bowl, mixing, and drawing out two of them.
(a)
What are the 10 possible outcomes (simple events)?
{(B, C), (B, M), (B, S), (C, M), (C, P), (C, S), (M, P), (M, S), (P, S)}
{(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, S), (C, M), (C, P), (C, S), (M, P), (M, S), (P, 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), (P, P), (B, S), (C, M), (C, P), (C, S), (M, P), (M, S), (P, S)}
(b)
From the description of the selection process, all simple events are equally likely. What is the probability of each simple
(c)
What is the probability that one of the committee members is the statistics department representative?
(d)
What is the probability that both committee members come from laboratory science departments?
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