1. Indicate true (T) or false (F).
(a) {1,2} ⊂ {2,1}
(b) {5,10} = {10,5}
(c) {0} ∈ (0, {0}}
2. Write the resulting set using the listing miethod.
(a) {1,2,3} ∩ {2,3,4}
(b) {1,2,3} U {2, 3, 4}
(c) {x|x2 = 25}
(d) For U = {1,2,3,4,5} and A = {2,3,4}, find A'.
3. A combination lock has 5 wheels, each labeled with the 10 digits from 0 to 9. How many 5-digit opening combinations are possible if no digit is repeated? If digits can be repeated? If successive digits must be different?
4. A group of 100 people touring Europe includes 42 people who speak French, 55 who speak German, and 17 who speak neither language. How many people in the group speak both French and German?
5. Evaluate the expression.
(a) P12,7
(b) C12,7
6. How many ways can a 3-person subcommittee be selected from a committee of 7 people?
How many ways can a president, vice-president, and secretary be chosen from a committee of 7 people?
7. From a standard 52-card deck, how many 7-card hands have exactly 5 spades and 2 hearts?
8. A basketball team has 5 distinct positions. Out of 8 players, how many starting teams are possible if
(a) the distinct positip,zo are taken into consideration?
(b) tne wstinot positi6ns'are not taken into consideration?
(c) the distinct- p6sitions are not taken into consideration. but either Mike or Ken (but not both) must start?
9. An experiment consists of drawing 1 card from a standard '52-carLdeck. What is the probability of drawing a club?
10. An experiment consists of dealing 5 cards from a standard 52-card deck. What is the vrobability of being dealt 2 Aces and 3 queens?
11. Compute the odds in favor of obtaining at leat 1 head when a single coin is tossed 3 times.
12. Compute the odds against obtaining a 3 or an even number in a single roll of a die.
13. A single card is draw from a standard 52Card deck. Calculate the probablity of and odds for drawing a black card or an ace.
14. What is the probability of getting at least 1 diamond in a 5-card hand dealt from a standard 52-card deck?
15. A card is drawn at random from a standard 52-card deck. Events G and H are G - the drawn card is black and H = the drawn card is divisible by 3 (face cards arc not valued).
(a) Find P(H|G).
(b) Test H and G for independence.
16. Let A be the event that all of a family's children are the same gender, and let B be the event that the family has at most 1 boy. Assuming the probability of having a girl is the same as the probability of having a boy (both 1/2), test events A and B for independence if
(a) the family has 2 children.
(b) the family has 3 children.
17. 2 balls are drawn in succession out of a box containing 2 red balls and 5 white balls. Let Ri, be the event that the ith ball is red, and let Wi; be the event that the ith ball is white. Construct a probability tree for this experiment and find the probability of each of the events R1 ∩ R2, R1 ∩ W2, W1 ∩ R2, and W1 ∩W2, given that the first ball drawn was not replaced before the second draw.
18. A pair of dice is rolled once. Suppose you lose $10 if a 7 turns up and win $11 if an 11 or 12 turns up. How much should you win or lose if any other number turns up in order for the game to be fair.
19. Five thousand tickets are sold at $1 each for a charity raffic. Tickets are to be drawn randomly and monetary prizes awarded as follows: 1 prize of $500, 3 prizes of $100, 5 prizes of $20, and 20 prizes of $5.
What is the expested value of this raffle if you buy 1 ticket?