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Chapter 6: Problem 27

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. 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 statistics department representative? d. What is the probability that both committee members come from laboratory science departments?

Short Answer

Expert verified
a. The 10 possible outcomes are: BC, BM, BP, BS, CM, CP, CS, MP, MS, PS. b. The probability of each simple event is 0.1. c. The probability that one of the committee members is the statistics department representative is 0.4. d. The probability that both committee members come from laboratory science departments is 0.1.

Step by step solution

01

Calculation of Possible Outcomes (simple events)

The total possible outcomes of drawing 2 students from 5 can be calculated as combinations of 5 students taken 2 at a time. This can be represented mathematically as \(C(n, k) = \frac{n!}{k!(n-k)!}\), where n is the total number and k is the number of items to select. In this case, \(C(5, 2) = \frac{5!}{2!(5-2)!} = 10\) possible outcomes. They are: BC, BM, BP, BS, CM, CP, CS, MP, MS, PS.
02

Probability of Each Simple Event

Since all outcomes are equally likely, the probability of each simple event occurring is the reciprocal of the total number of outcomes. This is calculated with the formula \(P(A) = \frac{1}{n}\), where P(A) is the probability of event A and n is the total number of outcomes. So, the probability of each simple event = \(\frac{1}{10}\).
03

Probability that a Committee Member is from the Statistics Department

We need to count combinations that include 'S'. From the list of 10 combinations, 4 of them (BS, CS, MS, PS) include 'S'. Using the formula in Step 2, the probability that one of the committee members is the statistics department representative is \( \frac{4}{10} = 0.4\).
04

Probability that both Committee Members are from Laboratory Science Departments

The laboratory science departments are Biology and Chemistry. Now, we are interested in the combinations that include only B and C. They are BC which is 1 of 10 outcomes. Hence, the probability that both committee members come from laboratory science departments is \(\frac{1}{10}=0.1\)

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Most popular questions from this chapter

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