Let’s rework example 2.32 from you textbook, but with different numbers. A 8 person committee consist of 5 women, including Margaret, and 3 men, including Anthony. If a subcommittee of 3 people is to be chosen at random to evaluate a new project. The subcommittee needs to include at least 1 women, but can’t consist entirely of women. (a) How many ways are there to select a subcommittee which consist of 1 man and 2 women? (b) How many ways are there to select a subcommittee which consist of 2 man and 1 women? (c) How many subcommittees satisfying the conditions can be selected?
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.
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Let’s rework example 2.32 from you textbook, but with different numbers. A 8 person committee consist of 5 women, including Margaret, and 3 men, including Anthony. If a subcommittee of 3 people is to be chosen at random to evaluate a new project. The subcommittee needs to include at least 1 women, but can’t consist entirely of women.
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(a) How many ways are there to select a subcommittee which consist of 1 man and 2 women?
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(b) How many ways are there to select a subcommittee which consist of 2 man and 1 women?
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(c) How many subcommittees satisfying the conditions can be selected?
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(d) How many subcommittees which include Anthony can be selected?
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(e) What is the probability that Anthony is included in the subcommittee
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(f) How many different subcommittees include Margaret?
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(g) How many different subcommittees include at least one of Anthony or Margaret? (Hint: Make sure that you do not count a committee more than once)
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(h) What is the probability that at least one of Anthony or Margaret are in the subcommittee?
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