Question

a researcher randomly selects 95 high - school swimmers and asks them which swim stroke is their strongest and which bathing suit brand they prefer, brand a or brand b. the two - way table displays the data. suppose one of the students is randomly selected. let b = the student prefers brand b and f = the students strongest stroke is freestyle.
which of the following is the correct value and interpretation of p(f|b)?
p(f|b)=0.51; given that the student prefers brand b, there is a 0.51 probability that their strongest stroke is freestyle.
p(f|b)=0.58; given that the student prefers brand b, there is a 0.57 probability that their strongest stroke is freestyle.
p(f|b)=0.51; given that the students strongest stroke is freestyle, there is a 0.51 probability that they prefer brand b.

swim stroke	breast	freestyle	butterfly	total
brand b	18	26	7	51
total	33	45	17	95

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(F|B)=\frac{P(F\cap B)}{P(B)}$. In terms of frequencies in a two - way table, $P(F|B)=\frac{n(F\cap B)}{n(B)}$, where $n(F\cap B)$ is the number of students who prefer brand B and have freestyle as their strongest stroke, and $n(B)$ is the number of students who prefer brand B.

Step2: Identify values from the table

From the two - way table, $n(F\cap B) = 26$ (the number in the cell where "Freestyle" row and "Brand B" column intersect), and $n(B)=51$ (the total number of students who prefer brand B).

Step3: Calculate the conditional probability

$P(F|B)=\frac{26}{51}\approx0.51$. The interpretation of $P(F|B)$ is: given that the student prefers brand B, there is a 0.51 probability that their strongest stroke is freestyle.

Answer:

$P(F|B) = 0.51$; given that the student prefers brand B, there is a 0.51 probability that their strongest stroke is freestyle.