## 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 2

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

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2022-02-02T13:45:11+00:00
2022-02-02T13:45:11+00:00 2 Answers
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## Answers ( )

Answer:The probability that a student passed the test given that they did not complete the assignment is [tex]\frac{15}{22}[/tex].

Step-by-step explanation:The probability of an event

Eis the ratio of the number of favorable outcomesn(E) to the total number of outcomesN.[tex]P(E)=\frac{n(E)}{N}[/tex]

The union of two events is:

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

The intersection of the complements of two events is:

[tex]P(A^{c}\cap B^{c})=1-P(A\cup B)[/tex]

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

[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]

Denote the events as follows:

= students who passed the testA= students who completed the assignmentBGiven:

N = 27

n (A) = 17

n (B) = 22

[tex]n(A^{c}\cap B^{c})[/tex] = 3

Compute the value of P (

A∪B) as follows:[tex]P(A^{c}\cap B^{c})=1-P(A\cup B)[/tex]

[tex]P(A\cup B)=1-P(A^{c}\cap B^{c})[/tex]

[tex]=1-\frac{3}{27}\\[/tex]

[tex]=\frac{24}{27}[/tex]

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

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

[tex]P(A\cap B)=P(A)+P(B)-P(A\cup B)[/tex]

[tex]=\frac{17}{27}+\frac{22}{27}-\frac{24}{27}\\[/tex]

[tex]=\frac{17+22-24}{27}[/tex]

[tex]=\frac{15}{27}[/tex]

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

[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]

[tex]=\frac{15/27}{22/27}[/tex]

[tex]=\frac{15}{22}[/tex]

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

Answer:17/22

Step-by-step explanation:my teacher said it was the answer