Question

This table shows how many sophomores and juniors attended two school events. What is the probability that the student attended the volleyball game, given that the student is a sophomore
A
B
C
or D

Answer 1

Answer:

B 0.55

Step-by-step explanation:

the student is a sophomore - so youre looking at the sophomore row, 77 sophomores total

the student attended the volleyball game - 42 sophomores attended the game

42 / 77 students total = about 0.55

Answer 2

Answer:

Option: B is the correct answer.

              B.   0.55

Step-by-step explanation:

Let A denote the event that the student is a sophomore.

and B denote the event that the student attend the volleyball game.

and A∩B denote the event that the student is a sophomore and attend volleyball game.

Let P denote the probability of an event.

We are asked to find the probability : P(B|A)

We know that:

$P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}$

Based on the table provided to us we have:

$P(A)=\dfrac{77}{137}$

and

$P(A\bigcap B)=\dfrac{42}{137}$

Hence, we have:

$P(B|A)=\dfrac{\dfrac{42}{137}}{\dfrac{77}{137}}$

i.e.

$P(B|A)=\dfrac{42}{77}=0.55$