20 politicians are having a tea party, 6 Democrats and 14 Republicans. To prepare, they need to choose: 3 people to set the table, 2 people to boil the water, 6 people to make the scones. Each person can only do 1 task. (Note that this doesn’t add up to 20. The rest of the people don’t help.) (a) In how many different ways can they choose which people perform these tasks? (b) Suppose that the Democrats all hate tea. If they only give tea to 10 of the 20 people, what is the probability that they only give tea to Republicans? (c) If they only give tea to 10 of the 20 people, what is the probability that they give tea to 9 Republicans and 1 Democrat?
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.
20 politicians are having a tea party, 6 Democrats and 14
Republicans. To prepare, they need to choose: 3 people to set the
table, 2 people to boil the water, 6 people to make the scones.
Each person can only do 1 task. (Note that this doesn’t add up to
20. The rest of the people don’t help.)
(a) In how many different ways can they choose which people
perform these tasks?
(b) Suppose that the Democrats all hate tea. If they only give tea
to 10 of the 20 people, what is the probability that they only give
tea to Republicans?
(c) If they only give tea to 10 of the 20 people, what is the
probability that they give tea to 9 Republicans and 1 Democrat?
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