There are 16 kids on a soccer team. The players are either boys or girls, and they either prefer playing offense or defense. There are 6 boys who prefer offense, 3 boys who prefer defense, 5 girls who prefer offense, and 2 girls who prefer defense.
Suppose you choose one player from the team at random. Let event A be that the player is a girl and event B be that the player prefers defense. Find P left parenthesis B vertical line A right parenthesis.
(1 point)
Responses
2 over 5
Image with alt text: 2 over 5
2 over 7
Image with alt text: 2 over 7
1 over 10
Image with alt text: 1 over 10
2 over 3
To find P(B|A), we need to calculate the probability of choosing a player who prefers defense given that the player is a girl.
Let's first find the probability of choosing a girl:
Total number of players = 16
Number of girls = 5 + 2 = 7
P(A) = Number of girls / Total number of players = 7 / 16
Now, let's find the probability of choosing a girl who prefers defense:
Number of girls who prefer defense = 2
P(B and A) = Number of girls who prefer defense / Total number of players = 2 / 16
Finally, we can calculate P(B|A) using the formula:
P(B|A) = P(B and A) / P(A)
= (2 / 16) / (7 / 16)
= 2 / 7
Therefore, P(B|A) = 2/7.