Question

There are 200 students in eleventh grade high school class. There are 40 students in the soccer team and 50 students in the basketball team. Out of these students there are 10 who play on both teams.

Let A be the event that a randomly selected student plays soccer and B be the event that student plays basketball. Based on this information answer the following questions.
What is P(A)?
What is P(B)?
What is P(A and B)?
What is P(A | B)?
Is P( A | B)= P(A)?

Answer 1

P(A) = 0.2

P(B) = 0.25

P(A&B) = 0.05

P(A|B) = 0.2

P(A|B) = P(A) = 0.2

Explanation:

P(A) is the probability that the selected student plays soccer.

Then:

`P(A)=(40)/(200)=0.2`

P(B) is the probability that the selected student plays basketball.

Then:

`P(B)=(50)/(200)=0.25`

P(A and B) is the probability that the selected student plays soccer and basketball:

`P(A\&B)=(10)/(200)=0.05`

P(A|B) is the probability that the student plays soccer given that he plays basketball. In this case, as it is given that he plays basketball only 10 out of 50 plays soccer:

`P(A|B)=(P(A\&B))/(P(B))=(10)/(50)=0.2`

P(A | B) is equal to P(A), because the proportion of students that play soccer is equal between the total group of students and within the group that plays basketball. We could assume that the probability of a student playing soccer is independent of the event that he plays basketball.