There are 300 students in a twelfth-grade high school class. 120of these students have at least one sister and 100 have at least one brother. Out of the students that have at least one brother, there are 40 who have at least one sister and one brother. Let A be the event that a randomly selected student in the class has a sister and B be the event that the student has a brother. Based on this information, answer the following questions.
What is P(A), left parenthesis, A, right parenthesis, the probability that the student has a sister?
What is P(B), left parenthesis, B, right parenthesis, the probability that the student has a brother?
What is P(A\text{ and }B)P(A and B), 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\text{ | }B)P(A | B)P, left parenthesis, A, start a 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?