Question

In a math class with 27 students, a test was given the same day that an assignment was due. There were 17 students who passed the test and 22 students who completed the assignment. There were 3 students who failed the test and also did not complete the assignment. What is the probability that a student passed the test given that they did not complete the homework

Answer 1

Answer:

The probability that a student passed the test given that they did not complete the assignment is $\frac{15}{22}$.

Step-by-step explanation:

The probability of an event E is the ratio of the number of favorable outcomes n (E) to the total number of outcomes N.

$P(E)=\frac{n(E)}{N}$

The union of two events is:

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

The intersection of the complements of two events is:

$P(A^{c}\cap B^{c})=1-P(A\cup B)$

The condition probability of an event given that another event has already occurred is:

$P(B|A)=\frac{P(A\cap B)}{P(A)}$

Denote the events as follows:

A = students who passed the test

B = students who completed the assignment

Given:

N = 27

n (A) = 17

n (B) = 22

$n(A^{c}\cap B^{c})$ = 3

Compute the value of P (A ∪ B) as follows:

$P(A^{c}\cap B^{c})=1-P(A\cup B)$

  $P(A\cup B)=1-P(A^{c}\cap B^{c})$

                  $=1-\frac{3}{27}$

                  $=\frac{24}{27}$

Compute the value of P (A ∩ B) as follows:

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

$P(A\cap B)=P(A)+P(B)-P(A\cup B)$

               $=\frac{17}{27}+\frac{22}{27}-\frac{24}{27}$

               $=\frac{17+22-24}{27}$

               $=\frac{15}{27}$

Compute the value of P (A | B) as follows:

$P(A|B)=\frac{P(A\cap B)}{P(B)}$

            $=\frac{15/27}{22/27}$

            $=\frac{15}{22}$

Thus, the probability that a student passed the test given that they did not complete the assignment is $\frac{15}{22}$.

Answer 2

Answer:

17/22

Step-by-step explanation:

my teacher said it was the answer