Suppose that a certain college class contains 44 students. Of these, 19 are sophomores, 27 are English majors, and 7 are neither. A student is selected at random from the class. (a) What is the probability that the student is both a sophomore and an English major? (b) Given that the student selected is a sophomore, what is the probability that he is also an English major? Write your responses as fractions. (If necessary, consult a list of formulas.)
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.
Given,
The event S is defined as the student is a sophomore and event E is defined as the student is a English major.
Totally there are 44 students out of which there are 19 sophomores, 27 English and 7 are neither.
The number of students who is both sophomore and English majors is,
The probability that the student is both a sophomore and English major is calculated as follows:
The probability that the student is both a sophomore and English major is 9/44.
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