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

The probability that a student passed the test given that they did not complete the assignment is .

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.

The union of two events is:

The intersection of the complements of two events is:

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

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

= 3

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

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

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

Thus, the probability that a student passed the test given that they did not complete the assignment is .

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step-by-step explanation: