Section 4.2 Exercises
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1 Section 4.2 Exercises 1. A company is to elect a secretary and a treasurer from the group of 30 members. How many ways can those two officers be elected? 2. Sandra has 9 shirts and 5 pairs of pants. How many different outfits can she make? 3. Area codes are made up of 3-digit numbers. a. If all numbers can be used for each digit, how many area codes are possible? b. How many area codes would be possible if repetition is not allowed? 4. A gymnasium has 5 different doors. How many ways can a person enter the gymnasium and then leave through a different door? 5. A license plate consists of 3 letters followed by 4 numbers. a. How many of these license plates are possible? b. How many plates are possible if repetition is not allowed? Evaluate: 6. 4! 7. 8! 8. 11! P P P P You have 9 books to place on a shelf, but you only have room for 5 of them. How many different ways can you arrange books on this shelf? 15. Sam has 6 favorite football teams, and every week he puts their flags on his flagpole in random order. a. How many different ways can he arrange the flags? b. If he only has room for 3 of the flags on his flagpole, how many different ways can they be arranged? 16. A baseball batting order is made up of 9 players. How many different batting orders are possible? 17. Seven runners are in a race. How many different ways can they finish in 1 st, 2 nd, and 3 rd place? Evaluate: 18. 7C C C C out of 8 students will be chosen to go on a field trip. How many different ways can they be selected? 23. Of the 15 players at an awards dinner, 3 of them will be given identical trophies. How many different ways can the trophies be given out? 24. A teacher chooses 5 of her 12 students to clean the room. In how many ways can the students be chosen? 25. A student must answer 5 of the 8 essay questions on a test. How many ways can she select 5 questions? 26. What is the difference between a permutation and a combination? Give an example of each. Section 4.3 Exercises For Exercises #1-11, a dime is flipped and a single die is rolled.
2 1. Use the counting principle to determine the total number of outcomes. 2. List the sample space of all possible outcomes. 3. Find the probability of getting Heads and a Find the probability of getting Tails and a Find the probability of getting Heads and an even number. 6. Find the probability of getting Heads and a number greater than or equal to Find the probability of getting Tails or a Find the probability of getting Tails or a number less than Find the odds against obtaining a Head. 10. Find the odds against obtaining a Find the odds in favor of obtaining an even number. For Exercises #12-16, a quarter is flipped and a penny is flipped. 12. Use the counting principle to determine the total number of outcomes. 13. List the sample space of all possible outcomes. 14. Find the probability of getting Tails on the quarter and Tails on the penny. 15. Find the probability of getting exactly one Tails. 16. Find the probability of getting no Tails. For Exercises #17-21, the letters of the word PRIME are written on slips of paper and placed into a hat. Two of these letters will be pulled out of the hat, without replacement, one after the other. 17. Use the counting principle to determine the total number of outcomes. 18. List the sample space of all possible outcomes. 19. Find the probability that the first letter is a vowel. 20. Find the probability that both letters are vowels. 21. Find the probability that neither letter is a vowel. For Exercises #22-26, a pair of dice is rolled and the sum of the faces is obtained. 22. Find the probability that the sum is 6.
3 23. Find the probability that the sum is odd. 24. Find the probability that the sum is divisible by Find the odds against the sum being Find the odds in favor of the sum being 4. For Exercises #27-31, data regarding the transportation of children to school is given in the table on the right. Use the information in the table, find: Bus Car Boys 10 5 Girls The probability that a student chosen at random is a girl. 28. The probability that a student chosen at random rides the bus. 29. The probability that a student chosen at random rides in a car. 30. The probability that a student chosen at random is a girl who rides the bus. 31. The probability that a student chosen at random is a boy who rides in a car. For Exercises #32-36, a bag of jellybeans contains 24 of them, with the colors as follows: Red = 5, Blue = 3, Orange = 7, Green = 4, Yellow = 2, Purple = Find the probability that a jellybean selected at random is orange. 33. Find the probability that a jellybean selected at random is green or yellow. 34. Find the probability that a jellybean selected at random is neither red nor purple. 35. Find the probability that a jellybean selected at random is anything but yellow. 36. Find the probability that a jellybean selected at random is black. For Exercises #37-45, a single card is drawn from a standard deck of 52 cards 37. Find the probability that the card is a red queen. 38. Find the probability that the card is a six. 39. Find the probability that the card is a black card. 40. Find the probability that the card is a red nine. 41. Find the probability that the card is an ace or a heart. 42. Find the probability that the card is an ace and a heart. 43. Find the probability that the card is a face card.
4 Section 4.4 Exercises 1. A jar of jellybeans contains 7 red, 5 orange and 3 green jellybeans. One is selected and replaced, and then another is selected. Find the probability that: a. The first jellybean is orange and the second is green. b. The first jellybean is red and the second is orange. c. The first jellybean is green and the second is red. d. Both jellybeans are orange. e. Both jellybeans are red. f. Both jellybeans are green. 2. A card is selected from a standard 52-card deck, and then another card is selected, without replacement. Find the probability that: a. The first card is a jack and the second is an ace. b. The first card is the jack of hearts and the second is an ace. c. The first card is a queen and the second is also a queen. d. The first card is a spade and the second card is also a spade. 3. Mr. Art, Mrs. Biology, Ms. Chemistry, Mr. Drama, and Mrs. English put their names into a hat. Three names will be drawn out, without replacement. Find the probability that: a. Ms. Chemistry is chosen first. b. Mrs. Biology or Mr. Drama is chosen first. c. Ms. Chemistry is chosen first, Mr. Art is chosen second, and Mrs. English is chosen third. 4. A bag contains 11 blue, 7 white, 4 red and 6 purple marbles. a. Find the probability that a single draw results in a white marble. b. Find the probability of getting two blue marbles on two draws, with replacement. c. Find the probability of getting two blue marbles on two draws, if replacement is not allowed. d. Find the probability of getting two red marbles on two draws, if replacement is not allowed. e. Find the probability of getting a white and then a purple marble, if replacement is not allowed. 5. A family will decide where they should have dinner randomly, and have the following options: Location: City, Suburbs, Rural Style: Sit-down, Buffet
5 Price: Expensive, Moderate, Cheap a. Use a tree diagram to find the probability that they will eat in the City. b. Find the probability that they will eat at a Buffet. c. Find the probability that they will eat at a Cheap Buffet in the Suburbs. d. Find the probability that they will eat at a Rural Sit-down restaurant that is either Expensive or Moderate. 6. A nickel is flipped and then it is flipped again. a. Use a tree diagram to show the sample space and the probabilities. b. Find the probability that both flips result in Heads. c. Find the probability that both flips result in Tails. d. Find the probability that the first flip is Heads and the second flip is Tails. e. Find the probability that at least one Heads is obtained. f. Find the probability that neither coin is Heads. 7. A family consists of four boys and two girls. Two of them will be picked, at random, to do yard work. a. Use a tree diagram to show the sample space and the probabilities. b. Find the probability that both people that will be doing yard work are girls. c. Find the probability that none of the people doing yard work are girls. d. Find the probability that exactly one of the people doing yard work is a girl. 8. A gumball machine contains 6 red and 4 blue gumballs. Two of them are purchased (without replacement). a. Use a tree diagram to show the sample space and the probabilities. b. Find the probability that at least one of the gumballs is red. c. Find the probability that exactly one of the gumballs is red. d. Find the probability that at least one of the gumballs is blue. e. Find the probability that exactly one of the gumballs is blue. f. Find the probability that the second gumball is red. 9. What is the difference between with and without replacement?
6 Section 4.5 Exercises 1. Given the spinner on the right: a. Find the expected value. b. What does this expected value mean? 2. Given the spinner on the right: a. Find the expected value. b. What does this expected value mean? 3. Five hundred tickets will be sold for a raffle, at a cost of $2 each. The prize for the winner is $750. What is the expected value of a ticket for someone playing this raffle? 4. Four baseball caps are on a table. One cap has a $1 bill under it, another has a $5 bill, another has a $50 bill, and the last one has a $100 bill. You can select one cap, and keep the amount of money that is underneath. a. What is the expected value for playing this game? b. If this game cost $45 to play and you played it a large number of times, would you expect to win or lose money? c. If this game cost $45 to play and you played it 100 times, what would be the expected net profit or loss? 5. An American roulette wheel contains slots with numbers from 1 through 36, and slots marked 0 and 00. Eighteen numbers are red and eighteen numbers are black. The 0 and 00 are green. You place a $1 bet, betting that the result of the spin will be green. If you win, you win $17. a. What is the expected value of this bet? Round your answer to the nearest hundredth. b. What does this expected value mean?
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