There are 210 students in a twelfth grade high school class. 90 of these students have at least one sister and 105 have at least

I can answer top 3. P(sister) would be 9/21

P(brother) would be 1/2

P(both) would be 195/210

P(B | A), the conditional probability that the student... Out of 210 students, 90 have at least one sister. There are 45 who have at least one sister and one brother. \(\dfrac{45}{90}\) simplifies to \(\dfrac{1}{2}\). 

- PM

There are 210 students in a twelfth grade high school class. 90 of these students have at least one sister and 105 have at least one brother. Out of these, there are 45 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), the probability that the student has a sister? _____    \(\frac{90}{210}=\frac{3}{7}\)

What is P(B), the probability that the student has a brother?_____   \(\frac{105}{210}=\frac{1}{2}\)

What is P(A and B), the probability that the student has a sister and a brother? _____  \(\frac{45}{210}=\frac{3}{14}\)

What is P(B | A), the conditional probability that the student has a brother given that he or she has a sister?   \(\frac{45}{90}=\frac{1}{2}\)

Is P(B | A)=P(B)?   YES   Are the events A and B independent?   Yes I think they are independent.

Here is the corresponding Venn diagram.