Question

A teacher categorized students by whether they regularly completed their homework (or not) and whether they passed the course (or not). The data are in the table below.
Completed Homework Did not Complete Homework Total
Passed the Course 25 7 32
Did not Pass the Course 5 18 23
Total 30 25 55
A student from the class is randomly selected. Determine the following probabilites. Enter your results as percents rounded to two decimal places.
What is the probability a student passed the course given that they completed their homework?

%
What is the probability a student passed the course given that they didn't complete their homework?

28
Correct%
What is the probability a student completed their homework given that they passed the course?

%
What is the probability a student didn't complete their homework given that they didn't pass the course?

%

Answer 1

Probabilities are used to determine the chances of an event.

Let P represents the event that a student passes the course, and C represents the event that a student completes the assignment

(a) The probability a student passed the course given that they completed their homework?

From the table, we have:

$\mathbf{n(P\ n\ C) = 25}$

$\mathbf{n(C) = 30}$

So, the required probability is:

$\mathbf{Pr = \frac{n(P\ n\ C)}{n(C)}}$

This gives

$\mathbf{Pr = \frac{25}{30}}$

$\mathbf{Pr = 0.8333}$

Express as percentage

$\mathbf{Pr = 83.33\%}$

Hence, the probability a student passed the course given that they completed their homework is 83.33%

(b) The probability a student passed the course given that they didn't complete their homework

From the table, we have:

$\mathbf{n(P\ n\ C'= 7}$

$\mathbf{n(C') = 25}$

So, the required probability is:

$\mathbf{Pr = \frac{n(P\ n\ C')}{n(C')}}$

This gives

$\mathbf{Pr = \frac{7}{25}}$

$\mathbf{Pr = 0.28}$

Express as percentage

$\mathbf{Pr = 28\%}$

Hence, the probability a student passed the course given that they didn't complete their homework is 28%

(c) The probability a student completed their homework given that passed the course?

From the table, we have:

$\mathbf{n(P\ n\ C) = 25}$

$\mathbf{n(P) = 32}$

So, the required probability is:

$\mathbf{Pr = \frac{n(P\ n\ C)}{n(P)}}$

This gives

$\mathbf{Pr = \frac{25}{32}}$

$\mathbf{Pr = 0.78125}$

Express as percentage

$\mathbf{Pr = 78.125\%}$

Approximate

$\mathbf{Pr = 78.13\%}$

Hence, the probability a student completed their homework given that they passed the course is 78.13%

(d) The probability a student didn't complete their homework given that they didn't pass the course

From the table, we have:

$\mathbf{n(P'\ n\ C'= 18}$

$\mathbf{n(P) = 23}$

So, the required probability is:

$\mathbf{Pr = \frac{n(P'\ n\ C')}{n(P')}}$

This gives

$\mathbf{Pr = \frac{18}{23}}$

$\mathbf{Pr = 0.7826}$

Express as percentage

$\mathbf{Pr = 78.26\%}$

Hence, the probability a student didn't complete their homework given that they didn't pass the course is 78.26%

Read more about probabilities at:

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