For diseases X, Y, and Z, if two carriers of the disease have a child, the child has a .25 chance of having the disease and .75 chance of not having the disease. Suppose two parents are carriers for all three diseases (X, Y and Z). The probability of inheriting any disease is independent of inheriting the other diseases. a) What is the probability that their first child does not have any of the diseases? b) What is the probability that their first child only has disease Y? c) What is the probability that their first child has two of three diseases?

Kevin is playing basketball with joy. Based on existing experience, kevin generally managed to make 8 free throws out of 10 throws. Unlike Kevin, generally joy only managed to make 3 free throws out of 10 throws. That afternoon, the two of them competed with each other for free throws. If it is assumed that both Kevin and Joy are free throws and have an equal chance of entering the ring, a. What is the probability that out of 5 free throws made by Joy, only two make it into the ring? b. What is the probability that Kevin's third throw is a free sheet that goes into the ring? c. What is the probability that Joy's sixth throw is the second free throw that makes it into the ring?

Composite blood testing is sometimes used to save costs.  A Hepatitis-C composite blood test means that when several blood samples are mixed together and tested for Hepatitis- C.  The probability of testing positive for Hepatitis-C in a certain population is 0.490.  If 4 bloodsamples are mixed together, what is the probability that composite sample would be positive (in other words, what is the probability that at least one of the people in the group is positive for Hepatitis-C)?

3. A retailer sells two brands of batteries that experience indicates are equal in demand. If he stocks two of each brand (which means he has 4 batteries in his store), what is the probability that a customer seeking to purchase two batteries, purchases the same brand? 1/3 2/3 01/2 1/4

Suppose that each time Bar-bie throws a dart, she has a 3/4 probability of getting a bullseye. If Barbie shoots three darts, what is the probability that she gets a bullseye on at least two of them?

8 Suppose disease X can be passed from father to child. If a father has the disease, each child has a 1/2 chance of having it too (independent of whether any other children do). If a father doesn't have the disease, none of their children will. Alexei is a father, and there's a 1/4 chance he has disease X. What is the probability Alexei has disease X if he has 2 children and neither one has the disease?

Suppose that there is a white urn containing two white balls and three red balls and there is a red urn containing one white ball and two red balls. An experiment consists of selecting at random a ball from the white urn and then​ (without replacing the first​ ball) selecting at random a ball from the urn having the color of the first ball. Find the probability that the second ball is red. The probability of the second ball being red is?