Scenario 1 A basket contains 3 red and 4 green balls. A random experiment is performed such that a ball is randomly drawn from the basket, replaced back in the basket and then again a ball is randomly drawn from the basket. Let X is a random variable containing the count of red colored balls at the end of two trials. Scenario 2 A basket contains 3 red and 4 green balls. A random experiment is performed such that a ball is randomly drawn from the basket, not replaced back in the basket and then again a ball is randomly drawn from the basket. Let X is a random variable containing the count of green colored balls at the end of two trials. Now answer the following questions. Compare the two scenarios by showing probability tree diagrams of the two. Examine and comment on the shape of the distribution for the two scenarios.
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.
Scenario 1
A basket contains 3 red and 4 green balls. A random experiment is performed such that a ball is randomly drawn from the basket, replaced back in the basket and then again a ball is randomly drawn from the basket. Let X is a random variable containing the count of red colored balls at the end of two trials.
Scenario 2
A basket contains 3 red and 4 green balls. A random experiment is performed such that a ball is randomly drawn from the basket, not replaced back in the basket and then again a ball is randomly drawn from the basket. Let X is a random variable containing the count of green colored balls at the end of two trials.
Now answer the following questions.
- Compare the two scenarios by showing
probability tree diagrams of the two.
Examine and comment on the shape of the distribution for the two scenarios.
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