Answer: Option D
[tex]P (B | A) =\frac{4}{5}[/tex]
Step-by-step explanation:
Call A to the event in which a student advances to the second round.
We know that:
[tex]P (A) = 75\% = 0.75[/tex]
Call B the event in which a student advances to the third round.
We know that:
[tex]P (B) = 60\% = 0.6[/tex]
We then look for the probability of B given A. This is:
[tex]P (B | A) =\frac{P(B\ and\ A)}{P(A)}[/tex]
In this case, the probability of B and A is equal to the probability of B, since the students who advance to the third round also advanced to the second round before
[tex]P (B | A) =\frac{P(B)}{P(A)}[/tex]
[tex]P (B | A) =\frac{0.6}{0.75}[/tex]
[tex]P (B | A) =\frac{4}{5}[/tex]
