There are 210
210210 students in a twelfth grade high school class.
90
9090 of these students have at least one sister and
105
105105 have at least one brother. Out of these, there are
45
4545 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
(
B
|
A
)
P(B | A)P, left parenthesis, B, start text, space, vertical bar, space, end text, A, right parenthesis, the conditional probability that the student has a brother given that he or she has a sister?

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