There are 300
300300 students in a twelfth grade high school class.
120
120120 of these students have at least one sister and
100
100100 have at least one brother. Out of the students that have at least one brother, there are
40
4040 who have at least one sister and one brother.
Let
A
AA be the event that a randomly selected student in the class has a sister and
B
BB be the event that the student has a brother. 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 has a sister?

What is
P
(
B
)
P(B)P, left parenthesis, B, right parenthesis, the probability that the student has a brother?

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 has a sister and a brother?

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 has a sister given that he or she has a brother?

Is
P
(
A
|
B
)
=
P
(
A
)
P(A | B)=P(A)P, left parenthesis, A, start text, space, vertical bar, space, end text, B, right parenthesis, equals, P, left parenthesis, A, right parenthesis? Are the events
A
AA and
B
BB independent?