Question 6

List the sample space.

1) Use a tree diagram showing all possible results when a die is rolled twice to list the ways of getting the sum of the numbers showing equal to 5.

Find the probability.

2) In a family with family with 4 children, excluding multiple births, what is the probability of having 2 girls and 2 boys, in that order? Assume that a boy is as likely as a girl at each birth.

Determine whether the following pair of events are mutually exclusive.

3) Let S = {a, b, c, d, e} be a sample space, E = {a, b, e}, and F = {b, c}. (a) Determine the events E ∪ F and E’ ∩ F’. (b) Are E ∪ F and E’ ∩ F’ mutually exclusive?

Use the addition rule to find the following probability. An experiment with outcomes, s1, s2, s3, s4 and s5 is described by the probability table below. Let E = {s1, s4} and F = {s1, s2, s3, s5}.

4) Compute Pr (E ∪ F). Use the addition rule to find the following probability.

5) A study conducted at a certain college shows that 62% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 7 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.

Use a tree diagram to find the probability. 6) A couple plans to have four children. Using a tree diagram, obtain the sample space. Then, find the

probability that the family has no boys.

Determine independence. Answer Yes or No. 7) The table shows the political affiliation of voters in one city and their positions on stronger gun control laws.

Stronger Gun Control

Are party affiliation and position on gun control laws independent? Find the expected value.

8) A contractor is considering a sale that promises a profit of $39,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $14,000 with a probability of 0.3. What is the expected profit?

Find the expected value.

9) Suppose that 1,000 tickets are sold for a raffle that has the following prizes: one $300 prize, two $100 prizes, and one hundred $1 prizes. What is expected value of a ticket?

Use the conditional probability formula to answer the following question. The graduates at a southern university are shown in the table.

A student is selected at random from the graduating class. 10) Find the probability that the student is female, given that the student is receiving an education degree,

P (F|E).

11) A normal distribution of test scores has a mean of 38 and a standard deviation of 6. What percent of the students scored between 30 and 45?

Normal Distribution