a- Use the given probabilities to construct a hypothetical 1000 table with columns corresponding to whether or not a student prepared properly for their final exams and rows corresponding to whether the student passes the course or not. b- Use the table to calculate the following probabilities i. The probability of preparing for the final exam or passing the course. ii. The probability of not preparing for the final exam nor passing the course. c- Are the events P(P) and P(S) independent? Justify your answer. d- Are the events P(P) and P(not S) mutually exclusive? Justify your answer.
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 school, students were asked if they prepared properly for their final exams, and if they passed the given
course.
80% of the students said they prepared properly for the exams, and 75% of them passed the exam.
70% of the students both prepared and pass the exams.
Consider the following
P = prepared properly for the final exam.
S = passed the given course
a- Use the given probabilities to construct a hypothetical 1000 table with columns corresponding to whether
or not a student prepared properly for their final exams and rows corresponding to whether the student
passes the course or not.
b- Use the table to calculate the following probabilities
i. The probability of preparing for the final exam or passing the course.
ii. The probability of not preparing for the final exam nor passing the course.
c- Are the events P(P) and P(S) independent? Justify your answer.
d- Are the events P(P) and P(not S) mutually exclusive? Justify your answer.
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