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Worksheet: Independent and Dependent Events Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. What is the probability that three standard dice rolled simultaneously will all land with the same the same number facing up? a. b. c. d. ____ 2. Suppose you simultaneously roll a standard die and spin a spinner that is divided into 10 equal sectors, numbered 1 to 10. What is the probability of getting a 4 on both the die and the spinner? a. b. c. d. ____ 3. Suppose you simultaneously roll a standard die and spin a spinner with eight equal sectors, numbered 1 to 8. What is the probability of both rolling an even number and spinning an odd number? a. b. c. d. ____ 4. A coin is flipped and a card is drawn from a standard deck of cards. What is the probability of getting both heads and a red face card? a. b. c. d. ____ 5. Which of the following statements is false? a. The product rule for independent events states that b. ____ ____ ____ . If event X is dependent on event Y, then . c. If event X is dependent on event Y, then . d. If event X is dependent on event Y, then . 6. If Mike does his mathematics homework today, the probability that he will do it tomorrow is 0.8. The probability that he will do his mathematics homework today is 0.7. What are the odds that he will do it both today and tomorrow? a. 4:1 b. 8:7 c. 3:2 d. 14:11 7. A bag contains three green marbles and four black marbles. If you randomly pick two marbles from the bag at the same time, what is the probability that both marbles will be black? a. b. c. d. 8. What is the probability of rolling a total of 7 in two rolls of a standard die if you get an even number on the first roll? a. b. c. d. Short Answer 9. Lesley-Anne estimates that she has a 75% chance of passing physics and an 80% chance of passing English. Assuming that {passing English} and {passing Physics} are independent events, a) what is the probability that Lesley-Anne will pass only one of these two subjects? b) what are the odds in favour of Lesley-Anne failing both subjects? 10. If a satellite launch has a 97% chance of success, what is the probability of three consecutive successful launches? 11. Carrie is a kicker on her rugby team. She estimates that her chances of scoring on a penalty kick during a game are 75% when there is no wind, but only 60% on a windy day. If the weather forecast gives a 55% probability of windy weather today, what is the probability of Carrie scoring on a penalty kick in a match this afternoon? 12. A bag contains three white marbles, five green marbles, and two red marbles. What are the odds in favour of randomly picking both red marbles in the first two tries? Assume that the first marble picked is not put back into the bag. 13. If the probability of the Rangers defeating the Eagles in a hockey game is Rangers will win two consecutive games against the Eagles? , what is the probability that the 14. Statsville has two computer-controlled traffic lights on the road between the main street and the highway. The probability of getting a red light at the first traffic light is 0.45, and the probability of getting a red light at the second one is 0.20 if you had been stopped by a red light at the first one. What is the probability of being stopped by red lights at both intersections? Problem 15. A survey at a school asked students if they were ill with a cold or the flu during the last month. The results were as follows. None of the students had both a cold and the flu. Females Males Cold 32 25 Flu 18 19 Healthy 47 38 Use these results to estimate the probability that a) a randomly selected student had a cold in the last month b) a randomly selected female student was healthy last month c) a randomly selected student who had the flu last month is male d) a randomly selected male student had either a cold or the flu last month 16. To get out of jail free in the board game MONOPOLY®, you have to roll doubles with a pair of standard dice. Determine the odds in favour of getting out of jail on your first or second roll. 17. At an athletic event, athletes are tested for steroids using two different tests. The first test has a 93.0% probability of giving accurate results, while the second test is accurate 87.0% of the time. For a sample that does contain steroids, what is the probability that a) neither test shows that steroids are present? b) both tests show that steroids are present? c) at least one of the tests detects the steroids? 18. A test for the presence of E. coli in water detects the bacteria 97% of the time when the bacteria is present, but also gives a false positive 2% of the time, wrongly indicating the presence of E. coli in uninfected water. If 10% of the water samples tested contain E. coli, what is the probability that a test result indicating the presence of the bacteria is accurate? 19. A study on the effects that listening to loud music through headphones had on teenagersâ€™ hearing found that 12% of those teenagers in the sample who did listen to music in this way showed signs of hearing problems. If 60% of the sample reported that they listened to loud music on headphones regularly, and 85% of the sample were found not to have hearing problems, are the events {having hearing problems} and {listening to loud music on headphones} independent? Explain your reasoning. Worksheet: Independent and Dependent Events Answer Section MULTIPLE CHOICE 1. ANS: OBJ: 2. ANS: OBJ: 3. ANS: OBJ: 4. ANS: OBJ: 5. ANS: OBJ: 6. ANS: OBJ: 7. ANS: OBJ: 8. ANS: OBJ: B Section 6.4 D Section 6.4 C Section 6.4 C Section 6.4 C Section 6.4 D Section 6.4 B Section 6.4 B Section 6.4 PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: 1 REF: Knowledge & Understanding Dependent and independent events 1 REF: Knowledge & Understanding Dependent and independent events 1 REF: Knowledge & Understanding Dependent and independent events 1 REF: Knowledge & Understanding Dependent and independent events 1 REF: Knowledge & Understanding Dependent and independent events 1 REF: Knowledge & Understanding Dependent and independent events 1 REF: Knowledge & Understanding Dependent and independent events 1 REF: Knowledge & Understanding Dependent and independent events SHORT ANSWER 9. ANS: a) 0.35 b) 1:19 PTS: 1 10. ANS: About 91% REF: Applications OBJ: Section 6.4 TOP: Dependent and independent events PTS: 1 11. ANS: REF: Applications OBJ: Section 6.4 TOP: Dependent and independent events PTS: 1 12. ANS: REF: Applications OBJ: Section 6.4 TOP: Dependent and independent events The probability of picking the two red marbles in the first two picks is . Therefore, the odds in favour of picking the two red marbles are 1:44. PTS: 1 13. ANS: REF: Applications OBJ: Section 6.4 TOP: Dependent and independent events PTS: 1 14. ANS: 9.0% REF: Applications OBJ: Section 6.4 TOP: Dependent and independent events PTS: 1 REF: Applications OBJ: Section 6.4 TOP: Dependent and independent events PROBLEM 15. ANS: a) b) Using the conditional probability formula, : c) Restricting the sample space to only those who had the flu, d) Restricting the sample space to only males, PTS: 1 16. ANS: REF: Applications OBJ: Section 6.4 The probability of rolling doubles on the first roll is roll is . TOP: Dependent events . The probability of not rolling doubles on the first Therefore, the probability of rolling doubles on the second roll is . The probability of rolling doubles on the first roll or the second roll is . Thus, the odds in favour of getting out of jail on either the first or second try are 11:25. PTS: 1 17. ANS: REF: Applications OBJ: Section 6.4 TOP: Dependent and independent events a) b) c) PTS: 1 REF: Applications | Communication OBJ: Section 6.4 TOP: Dependent and independent events 18. ANS: If 10% of the water samples contain E. coli and the test is 97% effective, then However, 90% of the samples do not contain E. coli and these samples will test positive 2% of the time, so The overall probability of a positive test result is 0.097 + 0.018 = 0.115. Therefore, the conditional probability formula gives The probability is 84% that a positive test result is accurate. PTS: 1 REF: Thinking/Inquiry/Problem Solving OBJ: Section 6.4 TOP: Dependent and independent events 19. ANS: If events A and B are independent, . Since P(hearing problems) = 0.15 and P(listening to loud music on headphones) = 0.60, then However, the observed probability of having hearing problems and listening to loud music on headphones is 0.12, which is significantly higher than 0.09. Therefore, these two events cannot be independent if the survey results are accurate. PTS: 1 REF: Communication | Thinking/Inquiry/Problem Solving OBJ: Section 6.4 TOP: Dependent and independent events