Question

In a large statistics course, 74% of the students passed the first exam, 72% of the students pass the second exam, and 58% of the students passed both exams. Assume a randomly selected student is selected from the class. If the student passed the first exam, what is the probability that they passed the second exam?

Answer 1

Answer:

Required probability is 0.784 .

Step-by-step explanation:

We are given that in a large statistics course, 74% of the students passed the first exam, 72% of the students pass the second exam, and 58% of the students passed both exams.

Let Probability that the students passed the first exam = P(F) = 0.74

     Probability that the students passed the second exam = P(S) = 0.72

     Probability that the students passed both exams = $P(F \bigcap S)$ = 0.58

Now, if the student passed the first exam, probability that he passed the second exam is given by the conditional probability of P(S/F) ;

As we know that conditional probability, P(A/B) = $\frac{P(A\bigcap B)}{P(B) }$

Similarly, P(S/F) = $\frac{P(S\bigcap F)}{P(F) }$ = $\frac{P(F\bigcap S)}{P(F) }$  {As $P(F \bigcap S)$ is same as $P(S \bigcap F)$ }

                          = $\frac{0.58}{0.74}$ = 0.784

Therefore, probability that he passed the second exam is 0.784 .