Probability Name _______________________________ Chapter 5 Homework Read each problem carefully. Write your answer in the blank, or circle the correct answer. 1. Why is the following not a valid probability model? (circle all that apply) a) This is not a probability model because P(green) < 0. b) This is not a probability model because the sum of the probabilities is not 1. c) This is not a probability model because P(red) > 0. d) This is not a probability model because P(brown) > 1. Color Red Green Blue Brown Yellow Orange Probability 0.3 –0.2 0.1 0.4 0.2 0.3 2. Describe the sample space of possible outcomes: Determining an athlete’s sport (Baseball (B), Soccer (S), Football (F)) and skill level (Low (L), Medium (M), High (H)) a) b) c) d) {BL, BM, SL, SM, FL, FM} {BL, BM, SL, SM, FL, FM, BL, BM, SL, SM} {BL, BM, BH, SL, SM, SH, FL, FM, FH, BL, BM, BH} {BL, BM, BH, SL, SM, SH, FL, FM, FH} 3. Suppose that event S has the following sample space: S = {1, 2, 3, 4}. Suppose all outcomes are equally likely. Compute P(E) if E = “an odd number less than 4”. Write your answer as a reduced fraction. P(E) = _______________ 4. A bag of 100 tulip bulbs purchased from a nursery contains 30 red tulip bulbs, 45 yellow tulip bulbs, and 25 purple tulip bulbs. What is the probability that a randomly selected tulip bulb is yellow? a) b) c) d) 3 /10 /20 1 /4 3 /2 9 5. In the game of roulette, suppose a wheel has 34 slots numbered 00, 0, 1, 2, 3, 4, …., 32. To play the game, a metal ball is spun around the wheel and falls into one of the numbered slots. Calculate the following probabilities. Write answers as reduced fractions. P(falls into slot 6) = __________ P(falls into an odd slot) = ___________ 6. In a national survey, college students were asked, “How often do you wear a seat belt when riding in a car driven by someone else?” The response frequencies appear in the following table. Response Never Rarely Sometimes Most of the time Always TOTAL Frequency 126 326 580 1,334 2,242 Response Never Rarely Sometimes Most of the time Always Probability 4,608 Complete/Construct the probability model above for seat-belt use by a passenger. Round answers to 3 decimals. Would you consider it unusual to find a college student who never wears a seat belt when riding in a car driven by someone else? a) b) c) d) No, because there were 126 people in the survey who said they never wear their seat belt. Yes, because P(never) < 0.05. No, because the probability of an unusual event is 0. No, because P(never) > 0.05. 7. Calculate P(Ec) if P(E) = 0.42. P(Ec) = ___________ 8. A golf ball is selected at random from a golf bag. If the golf bag contains 1 black ball, 6 green balls, and 13 yellow balls, calculate the following probabilities. Write your answers as reduced fractions. P(golf ball is black or green) = ____________ P(golf ball is not green) = ____________ 9. A standard deck of cards contains 52 cards. One card is selected from the deck. Calculate the following probabilities. Write your answers as reduced fractions. P(card is a queen or a king) = ____________ P( card is a queen or a king or a three) = ____________ P(card is a king or a diamond) = ____________ 10. The data in the following table show the association between cigar smoking and death from cancer for 133,261 men. Supposed one man is randomly chosen from the group. Calculate the following probabilities. Round your answers to 4 decimals. (Note: current cigar smoker means cigar smoker at time of death) Never Smoked Cigars Former Cigar Smoker Current Cigar Smoker Died from Cancer 870 71 145 Did not die from Cancer 117,594 7,981 6,600 P(died from cancer) = ____________ P(current cigar smoker) = ____________ P(died from cancer and current cigar smoker) = ____________ P(died from cancer or current cigar smoker) = ____________ P(never smoked cigars or did not die from cancer) = ____________ 11. The probability that a randomly selected male salamander will live to be 5 years old is 0.64126. If two male salamanders are randomly selected, what is the probability that both will live to be 5 years old? (round to 4 decimals) P(both live to be 5) = ____________ If four male salamanders are randomly selected, what is the probability that all four will live to be 5 years old? (round to 4 decimals) P(all four live to be 5) = ____________ If four male salamanders are randomly selected, what is the probability that at least one will live to be 5 years old? (round to 4 decimals) P(at least 1 lives to be 5) = ____________ 12. Suppose that a single card is drawn from a standard 52-card deck. Compute the following probabilities and leave your answers as reduced fractions. What is the probability that the card drawn is a club? P(club) = ____________ What is the probability that the card is a club given the card is black? P(club | black) = ____________ What is the probability that the card is a club given the card is a five? P(club | five) = ____________ 13. A recent poll of 2,278 randomly selected American adults were asked, “When you see an ad emphasizing that a product is “Made in the USA”, are you more likely to buy it, less likely to buy it, or neither?” The results of the survey, by age group, are given. Calculate the following probabilities and round your answers to 4 decimals. Likelihood More Likely Less Likely Neither 18–34 218 29 298 35–44 385 9 215 45–54 396 27 167 55+ 405 15 114 P(55+ | neither) = ____________ P(neither | 55+) = ____________ P(more likely | 18–34) = ____________ 14. Suppose that two cards are randomly selected from a standard 52-card deck. Compute the following probabilities and leave your answers as reduced fractions. P(first card is a queen, second card is a queen) = ____________ (sampling done WITHOUT replacement) P(first card is a queen, second card is a queen) = ____________ (sampling done WITH replacement) 15. A woman has eight skirts, ten blouses, and four belts. Assuming that they all match, how many different skirt-blouse-belt combinations can she wear? a) b) c) d) 22 320 216 1 16. Suppose Jim is going to burn a CD that will contain 10 songs. How many ways can Jim arrange the 10 songs on the CD? a) b) c) d) 10 10,000,000,000 3,628,800 100 17. A certain lock has 35 numbers on it. To open it, you turn counterclockwise to a number, then rotate clockwise to a second number, then counterclockwise to the third number, and so on until a four number lock combination has been effected. Repetitions are allowed. How many different lock combinations are there? a) 1,500,625 b) 1,256,640 c) 140 d) 10,000 What is the probability of guessing the lock combination of the first try? _____________ (write your answer as a fraction) 18. Suppose 16 cars start at a car race. How many ways can the top 3 cars finish the race? (ie, 1st place, 2nd place, 3rd place)? a) b) c) d) 48 3,360 560 20,922,789,890,000 19. Four members from a 60-person committee are to be selected randomly to serve as Chairperson, Vice-Chairperson, Secretary, and Treasurer. How many different leadership structures are possible? a) b) c) d) 240 11,703,240 487,635 205,320 20. How many samples of size 5 can be obtained from a population whose size is 46? a) b) c) d) 205,962,976 1,370,754 164,490,480 230