A teacher categorized students by whether they regularly completed their homework (or not) and whether they passed the course (o

Question

3 years ago

14

A teacher categorized students by whether they regularly completed their homework (or not) and whether they passed the course (o

r 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?

%

Mathematics

1 answer:

ella [17] · Answer 1 · 2022-09-20T16:43:37+03:00

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%