1) Free Response: Show all your work. Indicate clearly the methods you use because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.

The most frequent type of adverse reaction occurring with ibuprofen is gastrointestinal. In controlled clinical trials, the percentage of patients reporting one or more gastrointestinal complaints was 4%. Assume the probability that a randomly selected patient will suffer a gastrointestinal side effect after taking ibuprofen is 0.04 (Assume independence). A medical researcher randomly selects 4 migraine patients and prescribed ibuprofen.

A)What is the probability that at least one randomly selected patient will suffer a gastrointestinal side effect after taking ibuprofen?

B) What is the expected number of patients in this sample that will suffer a gastrointestinal side effect after taking ibuprofen? Interpret this value in the context of the problem.

C) Suppose the medical researcher had a large group of migraine patients. How many patients on average would need to be selected before finding someone who will suffer a gastrointestinal side effect after taking ibuprofen?

2) In a certain rat breeding program, 60% of the newborn rats are male. 30% of the male rats have curly tails while 45% of the female rats have curly tails. Use this information to find the following:

Let M represent the event that a randomly selected rat is a male and let C represent the event that a randomly selected rat has a curly tail.

Answer the following showing clearly how you found your answer.

A) Find the probability that a randomly selected rat is male with a curly tail. ()=P(MC)=

B) Find the probability that a rat has a curly tail. P(C)=

C) Find the probability that the rat is a male given it has a curly tail. (|)=P(M|C)=