Question

1. Let A be the set whose elements are the months of the year that begin with the letter J. A = { }

2. Define a set that is empty. Let B be the set: _________________________________________________________________________ _________________________________________________________________________

3. The following data was collected from a survey of 350 San Antonio residents Are you a Spurs fan? YES NO Male 204 19 Female 113 14

a. How many males were surveyed?

b. How many spurs fans were surveyed?

c. How many San Antonians surveyed are not fans and male? d. How many San Antonians surveyed are fans or female?

e. How many San Antonians surveyed are fans or male? f. How many San Antonians surveyed are not fans or female?

4. Let

X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

A = {1, 2, 5, 7, 8, 10, 14, 15} and B = {2, 3, 5, 9, 10, 13} and C = {2, 7, 10, 12, 14, 15}

a. A ∩ C = b. A ∪ B =

c. B ∩ C = d. A ∩ B ∩ C =

5. Gilbert asked his group of 10 friends from middle school the following questions:

Do you ride the bus? Do you get picked up?

Their responses are shown in the Venn diagram below:

Bus Pickup

Jenna Ron Leslie

Rick Vic Debbie

Johnny Pablo

Use the Venn diagram to list the elements of each set.

a. The set of students who ride the bus

b. The set of students who get picked-up

c. The set of students who ride the bus or get picked up

d. The set of students who ride the bus and get picked up

e. The set of students who don’t ride the bus nor get picked up

f. The set of students who ride the bus but do not get picked up Jenna Rick Johnny Leslie Debbie Pablo

6. A group of 100 people touring Europe includes 51 people who speak French 57 who speak Polish, and 16 who speak neither language.

a. Construct a Venn diagram describing this situation.

b. How many people in the group speak both French and Polish?

7. A small combination lock on a suitcase has 4 wheels, each labeled with the 10 digits 0 to 9.

a. How many 4 digit combinations are possible if no digit is repeated?

b. If digits can be repeated?

c. If successive digits must be different?

8. A card is drawn from a standard 52-card deck. If the card is an ace, you win $12; otherwise, you lose $2. What is the expected value of the game?

9. Ten thousand raffle tickets are sold at $2 each for a local benefit. Tickets will be drawn at random and monetary prizes awarded as follows: 2 prizes of $1,000, 4 prizes of $500, and 10 prizes of $100. What is the expected value if you buy 1 raffle ticket?

10. An insurance company charges an annual premium of $75 for a $200,000 insurance policy against a house burning down. If the empirical probability that a house burns down in a given year is 0.0003, what is the expected value of the policy to the insurance company?

Answer 1