In a particular high school English class, 6 students are in both the school band and the chorus, 11 students are in the chorus but not the band, 5 students are in the band but not the chorus, and the remaining 4 students are not in either the band or the chorus. This information is displayed in the 2-way contingency table below Suppose that you pick a student at random from the class, and you notice that the student you picked is someone you saw performing in the band last week. What is the probability that the student is also in the chorus? (Write your answer as a decimal rounded to 3 decimal places.)
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.
In a particular high school English class, 6 students are in both the school band and the chorus, 11 students are in the chorus but not the band, 5 students are in the band but not the chorus, and the remaining 4 students are not in either the band or the chorus. This information is displayed in the 2-way contingency table below
Suppose that you pick a student at random from the class, and you notice that the student you picked is someone you saw performing in the band last week. What is the probability that the student is also in the chorus? (Write your answer as a decimal rounded to 3 decimal places.)
Given Data:
| In the band | Not in band | Total | |
| In Chorus | 6 | 11 | 17 |
| Not in Chorus | 5 | 4 | 9 |
| Total | 11 | 15 | 26 |
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