Answer :
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 = [tex]P(F \bigcap S)[/tex] = 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) = [tex]\frac{P(A\bigcap B)}{P(B) }[/tex]
Similarly, P(S/F) = [tex]\frac{P(S\bigcap F)}{P(F) }[/tex] = [tex]\frac{P(F\bigcap S)}{P(F) }[/tex] {As [tex]P(F \bigcap S)[/tex] is same as [tex]P(S \bigcap F)[/tex] }
= [tex]\frac{0.58}{0.74}[/tex] = 0.784
Therefore, probability that he passed the second exam is 0.784 .