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?** [[☃ math-keypad 1]] **What is $P(B)$, the probability that the student has a brother?** [[☃ math-keypad 2]] **What is $P(A\text{ and }B)$, the probability that the student has a sister and a brother?** [[☃ math-keypad 3]] **What is $P(B\text{ | }A)$, the conditional probability that the student has a brother given that he or she has a sister?** [[☃ math-keypad 4]] **Is $P(B\text{ | }A)=P(B)$? Are the events $A$ and $B$ independent?** [[☃ radio 1]]