Q:

At the Rolling Ridge School spelling bee, 75% of thecontestants advanced to the second round and 60% advancedto the third round. What is the probability that a randomlyselected contestant advanced to the third round given the samecontestant advanced to the second round?A. 3/20B. 9/20c. 7/15D. 4/5

Accepted Solution

A:
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]