1)One ball is drawn at random from a bag containing 2 red balls and 3 white balls. (Enter your probabilities as fractions.)

(a) What is the probability that the ball is red? (b) What is the probability that the ball is green? (c) What is the probability that the ball is red or white?

2)A six-sided die is rolled. Find the probability of getting a number greater than 0. (Enter your probability as a fraction.)

3)An urn contains three red balls numbered 1, 2, 3, three white balls numbered 4, 5, 6, and four black balls numbered 7, 8, 9, 10. A ball is drawn from the urn. (Enter your probabilities as fractions.)(a) What is the probability that it is red? (b) What is the probability that it is odd-numbered? (c) What is the probability that it is red and odd-numbered? (d) What is the probability that it is red or odd-numbered? (e) What is the probability that it is not black?

4)From a deck of 52 ordinary playing cards, one card is drawn. (Enter your probabilities as fractions.)(a) Find the probability that it is a jack. (b) Find the probability that it is a black card. (c) Find the probability that it is a heart.

5) If the probability that an event will occur is 4/11. (Enter your probabilities as fractions.)(a) What are the odds in favor of the event occurring? (b) What are the odds against the event occurring?

6)If the odds that a particular horse will win a race are 1:17, what is the probability of the following? (Enter your probabilities as fractions.)(a) that the horse will win the race (b) that the horse will lose the race

7)One card is drawn from a deck of 18 cards numbered 1 through 18. Find the following probabilities. (Enter your probabilities as fractions.)(a) Find the probability that the card is even and divisible by 3. (b) Find the probability that the card is even or divisible by 3.

8)An ordinary six-sided die is tossed. What is the probability of getting a number divisible by 3 or an even number? (Enter your probability as a fraction.)

9)One ball is drawn from a bag containing 6 red balls numbered 1-6 and 8 white balls numbered 7-14. Find the following probabilities. (Enter your probabilities as fractions.)(a) What is the probability that the ball is red and even-numbered? (b) What is the probability that the ball is red or even-numbered? (c) What is the probability that the ball not divisible by 4?

10)Of 100 students, 28 can speak French, 10 can speak German, and 4 can speak both French and German. If a student is picked at random, what is the probability that he or she can speak French or German? (Enter your probability as a fraction.)

11) A card is drawn from a deck of 52 playing cards. Given that it is a red card, what is the probability that it is the following? (Enter your probabilities as fractions.)

(a) a heart (b) a king

12)A bag contains 9 red balls numbered 1, 2, 3, 4, 5, 6, 7, 8, 9 and 6 white balls numbered 10, 11, 12, 13, 14, 15. One ball is drawn from the bag. What is the probability that the ball is red, given that the ball is odd-numbered? (Enter your probability as a fraction.)

13)A bag contains 5 red balls and 6 white balls. Two balls are drawn without replacement. (Enter your probabilities as fractions.)(a) What is the probability that the second ball is white, given that the first ball is red? (b) What is the probability that the second ball is red, given that the first ball is white? (c) Answer part (a) if the first ball is replaced before the second is drawn.

14) (a) A box contains 4 red balls, 3 white balls, and 3 black balls. Two balls are drawn at random from the box (with replacement of the first before the second is drawn). What is the probability of getting a red ball on the first draw and a white ball on the second? (Enter your probability as a fraction.) (b) Answer part (a) if the first ball is not replaced before the second is drawn. (Enter your probability as a fraction.)

15)Two balls are drawn from a bag containing 8 white balls and 4 red balls. If the first ball is replaced before the second is drawn, what is the probability that the following will occur? (Enter your probabilities as fractions.)(a) both balls are red (b) both balls are white (c) the first ball is red and the second is white (d) one of the balls is black

16) A red ball and 8 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting each of the following? (Enter your probabilities as fractions.)(a) a red ball on the first draw and a white ball on the second (b) 2 white balls (c) 2 red balls

17)One card is drawn at random from a deck of 52 cards. The first card is not replaced, and a second card is drawn. (Enter your probabilities as fractions.)(a) Find the probability that both cards are hearts. (b) Find the probability that the first card is a diamond and the second is a spade.

18) Compute ₅P₃. ₅P₃ =

19) Compute ₁₄P₅. ₁₄P₅ =

20) Compute ₃P₀. ₃P₀ =

21) How many 5-digit numbers can be formed from the digits 1, 2, 3, 5, 6, 8, and 9 if the following is true?(a) Each digit may be used once in each number. numbers (b) Each digit may be used repeatedly in each number. numbers

22)Seven horses are entered in a race. In how many ways can the horses finish? Assume no ties ways

23) An examination consists of 10 questions. If 9 questions must be answered, find the number of different orders in which a student can answer the questions. orders

24) A sailboat owner received 9 different signal flags with his new sailboat. If the order in which the flags are arranged on the mast determines the signal being sent, how many 3-flag signals can be sent? 3-flag signals

25) If 13 people are qualified for the next flight of a new space vehicle, how many different groups of 2 people can be chosen for the flight? groups

26) If a child is given cards with A, C, D, G, O, and T on them, what is the probability he or she could spell CAT by guessing the correct arrangement of 3 cards from the 6? (Enter your probability as a fraction.)

27) A poll asks voters to rank Social Security, economics, the war on terror, health care, and education in the order of importance.(a) How many rankings are possible? rankings (b) What is the probability that one reply chosen at random has the issues ranked in the order they appear on the survey? (Enter your probability as a fraction.)

28)The table defines a discrete probability distribution. Find the expected value of the distribution.

x	0	1	2	3
Pr(x)	3/16	3/16	5/16	5/16

29)A nonprofit organization sells chances for a $90,000 classic Mustang at $100 per ticket. It sells 1500 tickets and offers four prizes, summarized in the table. What are the expected winnings (or loss) for each ticket? (Round your answer to the nearest cent.)

Prizes	Amount
First	$90,000
Second	8,800
Third	2,300
Fourth	1,700

There is an expected ---Select--- winning loss of $ .