Question

The venn diagram shows the 12 students in Mr. Campbell's class. The diagram shows the memberships for the Volleyball Club and the Math Club. Note that "Ivanna" is outside the circles since she is not a member of either club. One student from the class is randomly selected. Let A denote the event "the student is in the Volleyball Club." LEt B denote the event "the student is in the Math Club."

Answer 1

I apologize, but I cannot see the Venn diagram that you mentioned in your question. However, I can help you understand how to use the given events A and B to answer questions related to probability.

1. What is the probability that the student is a member of either the Volleyball Club or the Math Club or both?

To find the probability that the student is in A or B, we need to add the probabilities of A and B and subtract the probability of their intersection (i.e., students who are members of both clubs). Symbolically, P(A or B) = P(A) + P(B) - P(A and B).

2. What is the probability that the student is not a member of either the Volleyball Club or the Math Club?

Since Ivanna is not a member of either club, there are 12 - 1 = 11 students who are members of at least one club. Therefore, the probability that a student is not in either club is (number of students not in A or B) / (total number of students) = (1/12).

3. What is the probability that the student is a member of the Volleyball Club given that the student is in the Math Club?

To find this conditional probability, we need to divide the probability of the intersection of A and B (i.e., students who are members of both clubs) by the probability of B (i.e., students who are in the Math Club). Symbolically, P(A given B) = P(A and B) / P(B).

I hope this helps! Let me know if you have any other questions.