Question

A professor has noticed that even though attendance is not a component of the grade for his class, students who attend regularly obtain better grades. In fact, 35% of those who attend regularly receive A's in the class, while only 5% of those who do not attend regularly receive A's. About 65% of students attend class regularly. Given that a randomly chosen student receives an A grade, what is the probability that he or she attended class regularly? (Round the answer to four decimal places.)

Answer 1

Answer:  Probability that she attended class regularly given that she receives A grade is 0.9286.

Step-by-step explanation:

Since we have given that

Probability of those who attend regularly receive A's in the class = 35%

Probability of those who do not regularly receive A's in the class = 5%

Probability of students who attend class regularly = 65%

We need to find the probability that she attended class regularly given that she receives an A grade.

Let E be the event of students who attend regularly.

P(E) = 0.65

And P(E') = 1-0.65 = 0.35

Let A be the event who attend receive A in the class.

So, P(A|E) = 0.35

P(A|E') = 0.05

So, According to question, we have given that

$P(E|A)=\dfrac{P(E)P(A|E)}{P(E)P(A|E)+P(E')P(A|E')}\\\\P(E|A)=\dfrac{0.65\times 0.35}{0.65\times 0.35+0.35\times 0.05}\\\\P(E|A)=\dfrac{0.2275}{0.2275+0.0175}=\dfrac{0.2275}{0.245}=0.9286$

Hence, Probability that she attended class regularly given that she receives A grade is 0.9286.