Suppose that 70% of the people coming out of a particular exit of 1000th Street Station are University affiliates. You wait at the exit and ask 10 people whether they are affiliates or not. What is the probability that the third, the fifth and the tenth person are affiliates? What is the probability that the third, the fifth and the tenth person are affiliates and all others are not? Suppose you keep asking people until you find 10 that are not affiliates, and then you go home. How many people do you have to ask on average until you can go home? - You can assume that the status (affiliate or not) of the people coming from the subway are independent. - For the last part: the ten non-affiliates do NOT have to come out consecutively. For example, if you find 9 non-affiliates, then 1 affiliate and then 1 more non-affiliate, that's enough: you can go home.
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.
Suppose that 70% of the people coming out of a particular exit of 1000th Street Station are University affiliates. You wait at the exit and ask 10 people whether they are affiliates or not.
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What is the
probability that the third, the fifth and the tenth person are affiliates? -
What is the probability that the third, the fifth and the tenth person are affiliates and all others are not?
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Suppose you keep asking people until you find 10 that are not affiliates, and then you go home. How many people do you have to ask on average until you can go home?
- You can assume that the status (affiliate or not) of the people coming from the subway are independent.
- For the last part: the ten non-affiliates do NOT have to come out consecutively. For example, if you find 9 non-affiliates, then 1 affiliate and then 1 more non-affiliate, that's enough: you can go home.
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