Chapter 4 - Practice Problems 1

Transcription

1 Chapter 4 - Practice Problems SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. ) Compare the relative frequency formula for finding probabilities to the classical formula for finding probabilities. How are the two formulas similar and how are they different? What special requirements does the classical approach have? ) 2) Sometimes probabilities derived by the relative frequency method differ from the probabilities expected from classical probability methods. How does the law of large numbers apply in this situation? 2) 3) On an exam on probability concepts, Sue had an answer of 3 8 how she knew that this result was incorrect. for one problem. Explain 3) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Express the indicated degree of likelihood as a probability value. 4) ʺThere is a 40% chance of rain tomorrow.ʺ 4) A) D) 4 5) ʺYou have one chance in ten of winning the race.ʺ 5) A) D) Answer the question. 6) On a multiple choice test with four possible answers for each question, what is the probability of answering a question correctly if you make a random guess? 6) A) D) 2

2 Find the indicated probability. 7) A sample space consists of 76 separate events that are equally likely. What is the probability of each? A) 76 0 D) 76 7) Answer the question, considering an event to be ʺunusualʺ if its probability is less than or equal to ) Is it ʺunusualʺ to get a sum of 2 when a pair of dice is rolled? 8) A) Yes No 9) Assume that a study of 300 randomly selected school bus routes showed that 276 arrived on time. Is it ʺunusualʺ for a school bus to arrive late? 9) A) No Yes From the information provided, create the sample space of possible outcomes. 0) Flip a coin three times. 0) A) HTT THT HTH HHH TTH TTT HHH HHT HTH HTT THH THT TTH TTT HHH HTT HTH TTT HTT THH HHT THT D) HHH TTT THT HTH HHT TTH HTH Determine whether the events are disjoint. ) Draw one ball colored red from a bag. Draw one ball colored blue from the same bag. ) A) No Yes 2) Find a ten dollar bill on the sidewalk. Find a ten dollar bill on the grass. 2) A) No Yes Estimate the probability of the event. 3) A polling firm, hired to estimate the likelihood of the passage of an up-coming referendum, obtained the set of survey responses to make its estimate. The encoding system for the data is: = FOR, 2 = AGAINST. If the referendum were held today, estimate the probability that it would pass. 3), 2, 2,,, 2,, 2, 2,,,, 2,, 2,,,, 2, A) D) 0.4 Find the indicated probability. 4) If P(A) = 3, find P(A). 6 4) A) D) 0 2

3 5) If you pick a card at random from a well shuffled deck, what is the probability that you get a face card or a spade? 5) A) D) ) The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency table below summarizes the results. 6) Waiting Time Number of (minutes) Customers If we randomly select one of the customers represented in the table, what is the probability that the waiting time is at least 2 minutes or between 8 and 5 minutes? A) D) ) A 6-sided die is rolled. Find P(3 or 5). 7) A) D) 3 8) 00 employees of a company are asked how they get to work and whether they work full time or part time. The figure below shows the results. If one of the 00 employees is randomly selected, find the probability that the person drives alone or cycles to work. 8). Public transportation: 6 full time, 8 part time 2. Bicycle: 4 full time, 4 part time 3. Drive alone: 30 full time, 34 part time 4. Carpool: 7 full time, 7 part time A) D)

4 Is Event B dependent or independent of Event A? 9) A: A green ball is drawn from a box with five balls and placed next to the box. B: A red ball is drawn next and placed next to the green one. 9) A) Independent Dependent Find the indicated probability. 20) If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years. 20) A) D) 334 2) A die with 8 sides is rolled. What is the probability of rolling a number less than 7? 2) A) D) 8 22) If a person is randomly selected, find the probability that his or her birthday is in May. Ignore leap years. 22) A) 3 3 D) 2 23) A class consists of 50 women and 3 men. If a student is randomly selected, what is the probability that the student is a woman? 23) A) D) ) In one town, 36% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both Democrats. 24) A) D) ) Find the probability of correctly answering the first 5 questions on a multiple choice test if random guesses are made and each question has 6 possible answers. 25) A) D)

5 Answer Key Testname: CH 4 SET ) In the relative frequency formula, the probabilities are determined by conducting an experiment, counting the number of occurrences of the event, and creating the ratio of number of occurrences to number of times the experiment was conducted. In the classical approach, a sample space of all of the possible simple events is created and the number of successes is compared to the number of different simple events. In the classical approach, each outcome must be equally likely. 2) The law of large numbers states that as an experiment is repeated again and again, the relative frequency probabilities tend to approach the actual probabilities expected from the classical approach. 3) Probabilities cannot exceed. 4) C 5) A 6) B 7) D 8) A 9) A 0) B ) B 2) A 3) A 4) C 5) C 6) B 7) D 8) C 9) B 20) D 2) A 22) A 23) A 24) D 25) C 5