Question

In a particular course, it was determined that only 70% of the students attend class on Fridays. From past data it was noted that 95% of those who went to class on Fridays pass the course, while only 10% of those who did not go to class on Fridays passed the course. If a student passes the course, what is the probability that they did not attend on Fridays?

Answer 1

Answer: Probability that students who did not attend the class on Fridays given that they passed the course is 0.043.

Explanation:

Since we have given that

Probability that students attend class on Fridays = 70% = 0.7

Probability that who went to class on Fridays would pass the course = 95% = 0.95

Probability that who did not go to class on Fridays would passed the course = 10% = 0.10

Let A be the event students passed the course.

Let E be the event that students attend the class on Fridays.

Let F be the event that students who did not attend the class on Fridays.

Here, P(E) = 0.70 and P(F) = 1-0.70 = 0.30

P(A|E) = 0.95, P(A|F) = 0.10

We need to find the probability that they did not attend on Fridays.

We would use "Bayes theorem":

`P(F\mid A)=(P(F).P(A\mid F))/(P(E).P(A\mid E)+P(F).P(A\mid F))\\\\P(F\mid A)=(0.30* 0.10)/(0.70* 0.95+0.30* 0.10)\\\\P(F\mid A)=(0.03)/(0.695)=0.043`

Hence, probability that students who did not attend the class on Fridays given that they passed the course is 0.043.