1. A box of cookies contains three chocolate and seven butter cookies. Miguel randomly selects a cookie and eats it. Then he randomly selects another cookie and eats it. (How many cookies did he take?)

a.Draw the tree that represents the possibilities for the cookie selections. Write the probabilities along each branch of the tree.

b.Are the probabilities for the flavor of the SECOND cookie that Miguel selects independent of his first selection? Explain.

c.For each complete path through the tree, write the event it represents and find the probabilities.

d.Let S be the event that both cookies selected were the same flavor. FindP(S).

e.Let Tbe the event that the cookies selected were different flavors. FindP(T) by two different methods: by using the complement rule and by using the branches of the tree. Your answers should be the same with both methods.

f.LetU be the event that the second cookie selected is a butter cookie. FindP(U). 6X8=48 marks

2. Fertile (female) cats produce an average of six litters per year. Suppose that one fertile, female cat is randomly chosen. In one year, find the probability she produces:

a. Find the probability that she has no litters in one year

b. Find the probability that she has at least two litters in a half year

c. Find the probability that she has exactly three litters in a half year 3X8=24 marks

3. According to The World Bank, only 69% of the population of Uganda had access to electricity as of 2009. Suppose we randomly sample 8 people in Uganda. Let X = the number of people who have access to electricity.

a. Find the probability that 5 people in the sample have access to electricity.

b. Find the probability that at most 6 people in the sample have access to electricity.

c. Find the probability that more than 6 people in the sample have access to electricity. 3X8=24 marks