Question

There are

150
150150 students in an eleventh grade high school class. There are
45
4545 students in the soccer team and
35
3535 students in the basketball team. Out of these students, there are
20
2020 who play on both teams.
Let
A
AA be the event that a randomly selected student in the class plays soccer and
B
BB be the event that the student plays basketball. Based on this information, answer the following questions.
What is
P
(
A
)
P(A)P, left parenthesis, A, right parenthesis, the probability that the student plays soccer?

What is
P
(
B
)
P(B)P, left parenthesis, B, right parenthesis, the probability that the student plays basketball?

What is
P
(
A
and
B
)
P(A and B)P, left parenthesis, A, start text, space, a, n, d, space, end text, B, right parenthesis, the probability that the student plays soccer and basketball?

What is
P
(
A
|
B
)
P(A | B)P, left parenthesis, A, start text, space, vertical bar, space, end text, B, right parenthesis, the conditional probability that the student plays soccer given that he or she plays basketball?

Answer 1

P(a)=0.3

P(b)=0.23

P(a&b)=0.13

P(a|b)=0.57

Explanation:

Girl can I say this was very hard to read try better next time

By using a venn diagram we can figure out that out of the 150, 45 play soccer, 35 play basketball, 20 play both, 25 play exclusively soccer and 15 play exclusively basketball and 60 students in total play either

Let A be the probability of a student playing soccer and B be the probability of a student playing basketball

P(A)= 45/150

P(B)=35/150

P(A&B)=20/150

P(A|B)= 20/35