Muscular dystrophy is a genetic disease caused by a mutation on the X chromosome. During reproduction this mutation arises spontaneously on each of the X chromosomes of the parents, independently and with probability u = 0.301. We can therefore view the production of a child as consisting of two probabilistic experiments. First, one of the two sex chromosomes is chosen with equal probability from each parent. Second, for each X chromosome that is chosen, the muscular dystrophy mutation arises independently with probability µ. All male children carrying the mutation will develop muscular dystrophy, whereas only females whose X chromosomes both carry the mutation will develop the disease. What is the probability that a child will develop the disease? Round your answer to five decimal places.

For the same class you were asked to do some research on transfers bt two-year and four-year colleges. According to federal data on the year-round student population, in 2015-16 49% of all students completing a degree at a four-year college had been enrolled in a two-year colleges in the previous 10 years. If you take a random sample of 10 of these graduates, what is the probability that exactly 4 of them will have been enrolled in a two-year college in the last 10 years?

A certain blood test is 99.5% effective at detecting Foreign Bloodborne Pathogens (such as the hepatitis virus) in human blood. If two people who take this test are selected at random, what is the probability both tests correctly detect a Foreign Bloodborne Pathogen? If ten people who take this test are selected at random, what is the probability all tests correctly detect a Foreign Bloodborne Pathogen? If 1,000 people who take this test are selected at random, what is the probability at least one test FAILS to detect a Foreign Bloodborne Pathogen?

A laboratory blood test is 95% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 1% of the healthy persons tested. That is, if a healthy person is tested, then, with probability 0.01, the test result will imply that he or she has the disease. If 0.5% of the population actually has the disease, calculate the probability that  a randomly selected person will get a positive test result

When a scientist conducted a genetics experiments with​ peas, one sample of offspring consisted of 915915 ​peas, with 718718 of them having red flowers. If we​ assume, as the scientist​ did, that under these​ circumstances, there is a 3 divided by 43/4 probability that a pea will have a red​ flower, we would expect that 686.25686.25 ​(or about 686686​) of the peas would have red​ flowers, so the result of 718718 peas with red flowers is more than expected. a. If the​ scientist's assumed probability is​ correct, find the probability of getting 718718 or more peas with red flowers. b. Is 718 peas with red flowers significantly​ high? c. What do these results suggest about the​ scientist's assumption that 3 divided by 43/4 of peas will have red​ flowers? a. If the​ scientist's assumed probability is​ correct, the probability of getting 718 or more peas with red flowers is nothing. ​(Round to four decimal places as​ needed.)

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?

A couple decides to have children. Both the mother and father are normally pigmented but are carriers of the recessive gene for albinism. Considering that the chance of the mother giving birth to a girl is 0.48 and for a boy is 0.52, what is the probability that the couple will have 1 normally pigmented boy, 2 albino girls, and 2 albino boys in any order?