7:24 1 SECTION 5.2 Some Probability I Done 3 of 6 SECTION 5.2 Some Probability Rules-Compound Events 221 from the book Canyon Country Arches and Bridges by F. A. Barnes. The height of the arch opening is rounded to the nearest foot. Height of arch, feet 3-9 10-29 30-49 50-74 75 and higher Number of arches in park 111 96 30 33 18 For an arch chosen at random in Arches National Park, use the preceding information to estimate the probability that the height of the arch opening is (a) 3 to 9 feet tall (b) 30 feet or taller (c) 3 to 49 feet tall (d) 10 to 74 feet tall (e) 75 feet or taller 17. | General: Roll Two Dice You roll two fair dice, a green one and a red one. (a) Are the outcomes on the dice independent? (b) Find P(5 on green die and 3 on red die). (c) Find P(3 on green die and 5 on red die). (d) Find P[(5 on green die and 3 on red die) or (3 on green die and 5 on red die)]. 18. | General: Roll Two Dice You roll two fair dice, a green one and a red one. (a) Are the outcomes on the dice independent? (b) Find P(1 on green die and 2 on red die). (c) Find P(2 on green die and 1 on red die). (d) Find P[(1 on green die and 2 on red die) or (2 on green die and 1 on red die)]. 19. | General: Roll Two Dice You roll two fair dice, a green one and a red one. (a) What is the probability of getting a sum of 6? (b) What is the probability of getting a sum of 4? (c) What is the probability of getting a sum of 6 or 4? Are these outcomes mutually exclusive? 20. General: Roll Two Dice You roll two fair dice, a green one and a red one. (a) What is the probability of getting a sum of 7? (b) What is the probability of getting a sum of 11? (c) What is the probability of getting a sum of 7 or 11? Are these outcomes mutually exclusive? Problems 21-24 involve a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four 10s, etc., down to four 2s in each deck. 21.| General: Deck of Cards You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. (a) Are the outcomes on the two cards independent? Why? (b) Find P(Ace on 1st card and King on 2nd). (c) Find P(King on 1st card and Ace on 2nd). (d) Find the probability of drawing an Ace and a King in either order. General: Deck of Cards You draw two cards from a standard deck of 22. 52 cards without replacing the first one before drawing the second. (a) Are the outcomes on the two cards independent? Why? (b) Find P(3 on 1st card and 10 on 2nd). 7:24 1 SECTION 5.2 Some Probability I Done 4 of 6 222 Chapter 5 ELEMENTARY PROBABILITY THEORY (c) Find P(10 on Ist card and 3 on 2nd). (d) Find the probability of drawing a 10 and a 3 in either ord. 23. | General: Deck of Cards You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back (a) Are the outcomes on the two cards independent? Why? (b) Find P(Ace on 1st card and King on 2nd). (c) Find P(King on Ist card and Ace on 2nd). (d) Find the probability of drawing an Ace and a King in either on General: Deck of Cards You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle the deck. 24. and reshuffle the deck. (a) Are the outcomes on the two cards independent? Why? (b) Find P(3 on Ist card and 10 on 2nd). (c) Find P(10 on Ist card and 3 on 2nd). (d) Find the probability of drawing a 10 and a 3 in either order. 25. | Marketing: Toys USA Today gave the information shown in thei i about ages of children receiving toys. The percentages represent all toys sold. Age (years) Percentage of Toys What is the probability that a toy is purchased for someone (a) 6 years old or older? (b) 12 years old or younger? (c) between 6 and 12 years old? (d) between 3 and 9 years old? 2 and under 15% 3-5 22% 6-9 27% 10-12 14% 13 and over 22% Interpretation A child between 10 and 12 years old looks at this probability distribution and asks "Why are people more likely to buy toys for kids older than I am [13 and over] than for kids in my age group [10–12]?" How would you respond? 26. | Health Care: Flu Based on data from the Statistical Abstract of the United States, 112th edition, only about 14% of senior citizens (65 years old or older) get the flu each year. However, about 24% of the people under 65 vears old get the flu each year. In the general population, there are 12.5% senior citizens (65 years old or older). (a) What is the probability that a person selected at random from the general population is a senior citizen who will get the flu this year? (b) What is the probability that a person selected at random from the general population is a person under age 65 who will get the flu this year? (c) Answer parts (a) and (b) for a community that is 95% senior citizens. (d) Answer parts (a) and (b) for a community that is 50% senior citizens. Focus Problem: Lie Detector Test In this problem, you are asked to solve part of the Focus Problem at the beginning of this chapter. In his book Chances: Risk and Odds in Everyday Life, James Burke says that there is a 72% chance a polygraph test (lie detector test) will catch a person who is, 1m fact, lying. Furthermore, there is approximately a 7% chance that the poly- graph will falsely accuse someone of lying. (a) Suppose a person answers 90% of a long battery of questions truthfully. What percentage of the answers will the polygraph wrongly indicate are lies? 27. (b) Suppose a person answers 10% of a long battery of questions with ies. What percentage of the answers will the polygraph correctly indicate are lies? ETIITI Andrey Burmakin/Shutterstock.com