Webwork Problems - 3.2 Conditional Probability and Independence

Conditional Probability - A and B

Pr [A|B]=3/4, Pr [A]= 1/2, Pr[B^1]= 3/4. Find Pr[B|A] and Pr [B|A^1].

Conditional Probability - Mice in a Cage

For this problem, assume there are 3 grey females, 4 grey males, 5 white females, and 2 white males. As in the book, the biologist selects two mice randomly.
What is the probability of selecting two males given that both are grey?
What is the probability of selecting 1 mouse of each gender given that both are grey?

Conditional Probability - Choosing Balls

Assume that the box contains 7 blue balls, 4 white balls, and 6 red balls, and that we choose two balls at random from the box. What is the probability of neither being blue given that neither is white?

Conditional Probability - Members of a Committee

For this problem, assume that the committee contains 6 men and 7 women and that three are selected at random for a subcommittee. What is the probability that the subcommittee consists of 2 men and 1 woman, given that it contains both men and women?

Conditional Probability - Venn Diagram

Suppose for this problem that Pr[E] = [3/20], Pr[F] = [3/10], and Pr[ E∩F' ] = [1/10]. What is Pr[E|F]? What is Pr[F|E]?

Conditional Probability - Venn Diagram II

Rework problem 3 from section 3.2 of your text, involving sets E and F. Suppose for this problem that:
Pr[E] = 3/4 and Pr[F] = 2/3. Just as in the book, Pr[ (E∪F)' ] = 0.
(1) What is Pr[E|F]?
(2) What is Pr[F|E]?