Transcript Document
Welcome to Survey of Mathematics Unit 7 16) Music Purchases At the Virgin Music store in Times Square, 60 people entering the store were selected at random and were asked to choose their favorite type of music. Of the 60, 12 chose rock, 16 chose country, 8 chose classical, and 24 chose something other than rock, country, or classical. Determine the empirical probability that the next person entering the store favors a) rock music. b) country music. c) something other than rock, country, or classical music. Solution 22. Grade Distribution Mr. Doole’s grade distribution over the past 3 years for a course in college algebra is shown in the chart below. Grade Number A 43 B 182 C 260 D 90 F 62 I 8 If Sue Gilligan plans to take college algebra with Mr. Doole, determine the empirical probability that she receives a grade of a) A. b) C. c) D or higher. Solution 14. Remote Control A TV remote control has keys for channels 0 through 9. If you select one key at random, a) what is the probability that you press channel 6? b) what is the probability that you press a key for an even number? c) what is the probability that you press a key for a number less than 7? Solution Select a Card In Exercises 17–26, one card is selected at random from a deck of cards. Determine the probability that the card selected is 18. a 5 or a 7. 22. a diamond. 26. a king and a club. Spin the Spinner In Exercises 27–30, assume that the spinner cannot land on a line. Determine the probability that the spinner lands on (a) red, (b) green, (c) yellow, (d) blue. 28) RED Yellow Green Toss a Die In Exercises 13–16, a die is tossed. Determine the odds against rolling 14. an odd number. Deck of Cards In Exercises 17–20, a card is picked from a standard deck of cards. Determine the odds against and the odds in favor of selecting 20. a card greater than 5 (ace is low). The odds against the Blue Streaks winning the basketball game are 7:5. What is the probability that the Blue Streaks win the game? a. c. 5 12 1 5 b. 7 12 d. 1 7 10. Expected Value. If on a $1 bet, Paul Goldstein’s expected value is $0.30, what is Paul’s expected value on a $5 bet? 26. Raffle Tickets One thousand raffle tickets are sold for $1 each. One prize of $800 is to be awarded. a) Rena Condos purchases one ticket. Determine her expected value. b) Determine the fair price of a ticket. You get to select one card at random from a standard deck of 52 cards. If you pick a king, you win $6. If you pick a queen, you lose $3 and if you pick a jack, you lose $2. Determine your expectation for this game. Selecting an Envelope In Exercises 33–36, a person randomly selects one of the five envelopes shown below. Each envelope contains a check that the person gets to keep. Determine the person’s expectation if the checks in the envelopes are as follows. 1 2 4 3 5 34. Four envelopes contain a $1000 check, and one envelope contains a $5000 check. 16. Three Coins Three coins are tossed. a) Determine the number of points in the sample space. b) Construct a tree diagram and list the sample space. Determine the probability that c) no heads are tossed. d) exactly one head is tossed. e) three heads are tossed. In Exercises 11–14, determine the indicated probability. 12. If P(A or B) = 0.9, P(A) = 0.7, and P(B) = 0.5 and, determine P(A and B). Roll a Die In Exercises 17–20, a single die is rolled one time. Determine the probability of rolling 18. an odd number or a number greater than 4. Select One Card In Exercises 21–26, one card is selected from a deck of playing cards. Determine the probability of selecting 22. a jack or a club. Select Two Cards In Exercises 27–34, a board game uses the deck of 20 cards shown. Two cards are selected at random from this deck. Determine the probability of the following a) with replacement. b) without replacement. 28. They both show the number 3. Selecting an Envelope In Exercises 49–56, consider the colored envelopes shown below. If one of the envelopes is selected at random, determine the probability that 50. an envelope other than a blue envelope is selected.