Venn Diagrams, Probability and Combinations

1. In an experiment, a pair of dice is rolled and the total number of points observed.
(a) List the elements of the sample space
(b) If A = { 2, 3, 4, 7, 8, 9, 10} and B = {4, 5, 6, 7, 8} list the outcomes which comprise each of the following events and also express the events in words: A, A  B, and A  B.
(c) Use Venn diagrams to show the different events.

2. (Three cards are drawn from a deck of 52 playing cards and not replaced. Find the probability of the following:
a) Getting three jacks
b) Getting an ace, a king, and a queen in order.
c) Getting a club, a spade, and a heart in order
d) Getting three clubs

3. The table below shows the number of tests taken by 30 randomly selected college sophomores

Number of tests taken Number of students

0 12
1 8
2 2
3 3
4 or more 5
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If a student is selected at random, find the probability
a) the student has taken exactly two tests
b) the student has taken at least two tests
c) the student has taken at most three tests
d) the student has taken 3 or fewer tests
e) the student has taken one or two tests.

4.
a) How many ways can a person select three appetizers and two soups if there are six appetizers and five soups on the dinner menu?
b) Three married couples have bought tickets for six seats in a row for a movie.
i) In how many ways can they be seated?
ii) In how many ways can they be seated if each couple is to sit together with the husband to the left of the wife?
iii) In how many ways can they be seated if each couple is to sit together?
iv) In how many ways can they be seated if all the men are to sit together and all the women are to sit together?

5. At a fair run by a local charity organization, it costs 50 cents to try one's luck in drawing an ace from a deck of 52 playing cards. What is the expected profit per customer, if they pay $4 if and only if a person draws an ace?

6. An artist entered two paintings (Lighthouse and Old Cathedral) in a show. He feels that the probabilities are, 0.15, 0.18, and 0.11, respectively, that he will sell the Lighthouse, the Old Cathedral, or both. What is the probability that he will sell either of the two paintings?

7. A group of children can be classified according to eye color (blue, brown, green), gender (male, female), and hobby (collecting stamps, collecting baseball cards, collecting shells, collecting stickers). How many possible different classifications are there? Use a tree diagram.

See attached file for full problem description.