Math 1342 Exam 2 Review

Transcription

1 Math 1342 Exam 2 Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) If a sportscaster makes an educated guess as to how well a team will do this season, he is using what type of probability? 2) If one tosses a coin enough times, the number of heads and tails will tend to even out. This is an example of the law of. 1) 2) 3) If the probability that it will rain tomorrow is 0.25, what is the probability that it will not rain tomorrow? 4) Find the probability of getting a number greater than 4 when a die is rolled one time. 5) A coin is tossed 758 times and comes up heads 409 times. Use the Empirical Method to approximate the probability that the coin comes up heads. 6) A survey asked 34,407 homeowners how many pets they owned. The results were as followed: 3) 4) 5) 6) Number of Pets Number of Homeowners , or more 649 Total 34,407 What is the probability that a sampled homeowner has more than 1 pet? 7) A single card is drawn from a deck. Find the probability of selecting a heart or a 8. 8) An apartment building has the following distribution of apartments: 1 bedroom 2 bedroom 3 bedroom 1st floor nd floor rd floor If an apartment is selected at random, what is the probability that it is on the 2nd floor or has 2 bedrooms? 7) 8) 1

2 9) In a recent semester at a local university, 500 students enrolled in both General Chemistry and Calculus I. Of these students, 66 received an A in general chemistry, 73 received an A in calculus, and 33 received an A in both general chemistry and calculus. 9) Find the probability that a randomly chosen student received an A in general chemistry or calculus or both. 10) If P(A) = 0.45, P(B) = 0.41, and P(A or B) = 0.86, are A and B mutually exclusive? 11) Let A, B and C be independent events with P(A) = 0.3, P(B) = 0.5, and P(C) = 0.4. Find P(A and B and C). 12) Let A and B be events with P(A) = 0.9, P(B) = 0.4, and P(A and B) = Are A and B independent? 13) A lot of 1000 components contains 250 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. 10) 11) 12) 13) Find P(B and A). 14) A fair coin is tossed four times. What is the probability that the sequence of tosses is HHHT? 15) Given eight students, three of which are female, if two students are selected at random, without replacement, what is the probability that both students are female? 16) Urn 1 contains 4 red balls and 5 black balls. Urn 2 contains 6 red balls and 5 black balls. Urn 3 contains 2 red balls and 6 black balls. If an urn is selected at random and a ball is drawn, find the probability it will be red. 17) Below are listed the numbers of engineers in various fields by sex. Choose one engineer at random. Find P(electrical male). Mechanical Electrical Biomedical Male Female ) 15) 16) 17) 18) It has been reported that 3% of all cars on the highway are traveling at speeds in excess of 70 mph. If the speeds of four random automobiles are measured via radar, what is the probability that at least one car is going over 70 mph? 18) 2

3 19) There are 3 blue balls, 5 red balls, and 2 white balls in a bag of balls. If a person selects two of the balls, what is the probability that the second one is blue given that the first one was white? 20) A box contains blue chips and red chips. A person selects two chips without 19) 20) replacement. If the probability of selecting a blue chip and a red chip is 1 4, and the probability of selecting a blue chip on the first draw is 5, find the 16 probability of selecting the red chip on the second draw, given that the first chip selected was a blue chip. 21) A store manager wants to display 4 different brands of toothpaste in a row. How many ways can this be done? 22) A business has seven locations to choose from and wishes to rank only the top three locations. How many different ways can this be done? 23) A furniture manufacturer offers bookcases in 5 different sizes and 3 different colors. If every color is available in every size, then the total number of different bookcases is 21) 22) 23) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 24) A club has 10 members. There are 720 ways that a chairperson, a secretary, and a treasurer can be selected from these 10 members. Assume a person can hold, at most, one office. A) False B) True 24) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 25) How many different ways can a teacher select 5 students from a class of 19 students to each perform a different classroom task? 26) If a menu has a choice of 5 appetizers, 3 main courses, and 3 desserts, how many dinners are possible if each includes one appetizer, one main course, and one dessert? 27) A certain system has two components. There are 6 different models of the first component and 11 different models of the second. Any first component can be paired with any second component. A salesman must select 2 of the first component and 3 of the second to take on a sales call. How many different sets of components can the salesman take? 25) 26) 27) 3

4 28) At the campus cafeteria, a diner can purchase a "meal deal" that consists of an entree, a side dish, and a dessert. There are 4 choices for the entree, 3 choices for the side dish, and 3 choices for dessert. How many different meal deals are possible? 29) A bookcase contains 2 statistics books and 5 biology books. If 2 books are chosen at random, the chance that both are statistics books is 30) If 40 tickets are sold and 2 prizes are to be awarded, find the probability that one person will win both prizes if that person buys exactly 2 tickets. 31) A student and a professor each choose a number between 1 and 9 (1 and 9 are both possible choices). What is the probability that the two choose the same number? 32) A committee consist of 10 women and 8 men. Three members are chosen as officers. What is the probability that all three officers are women? 33) Determine whether the table represents a discrete probability distribution. 28) 29) 30) 31) 32) 33) x P(x) ) The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. Find P(1 or more). 34) x P(x) ) Find the mean of the distribution shown below. 35) X P(X) ) What is the standard deviation of the following probability distribution? 36) X P(X)

5 37) If a gambler rolls two dice and gets a sum of 10, he wins $10, and if he gets a sum of three, he wins $20. The cost to play the game is $5. What is the expectation of this game? 38) An investor is considering a $20,000 investment in a start-up company. She estimates that she has probability 0.15 of a $10,000 loss, probability 0.15 of a $15,000 loss, probability 0.25 of a $25,000 profit, and probability 0.45 of breaking even (a profit of $0). What is the expected value of the profit? 39) Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. n = 9, p = 0.7, P(7 or more) 40) A student takes a true-false test that has 13 questions and guesses randomly at each answer. Let X be the number of questions answered correctly. Find P(Fewer than 4) 41) The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 45% of adult Australian sheep dogs weigh 65 pounds or more. A sample of 19 adult dogs is studied. What is the mean number of dogs who weigh 65 lb or more? 42) It is estimated that 40% of households own a riding lawn mower. A sample of 12 households is studied. What is the mean number of households who own a riding mower? 43) A die is rolled 360 times. Find the standard deviation of the number of times a 3 will be rolled. 44) The failure rate for taking the bar exam in Philadelphia is 41%. If 375 people take the bar exam, what is the mean for the number of failures? 45) A computer store has 75 printers of which 25 are laser printers and 50 are ink jet printers. If a group of 10 printers is chosen at random from the store, find the mean and variance of the number of ink jet printers. 46) The probability that a person will have 0, 1, or 2 dental checkups per year is 0.3, 0.6, and 0.1, respectively. If seven people are picked at random, what is the probability that two will have no checkups, four will have one checkup, and one will have two checkups in the next year? 37) 38) 39) 40) 41) 42) 43) 44) 45) 46) 5

6 47) In the instructor's answer book for a mathematics text, 8% of the answers are incorrect. Use the Poisson approximation to express the probability that there are exactly 2 incorrect answers for a homework set with 50 problems. 48) In a batch of 100 cell phones, there are, on average, 6 defective ones. If a random sample of 25 is selected, find the probability of 3 defective ones. 47) 48) 6

7 Answer Key Testname: MATH 1342 EXAM 2 REVIEW 1) subjective probability 2) large numbers 3) ) 1 3 5) ) ) 13 8) ) ) Yes 11) ) Yes 13) ) ) ) ) ) ) ) ) 24 22) ) 15 24) B 25) 1,395,360 26) 45 27) 6 C 2 11 C 3 28) 36 29)

8 Answer Key Testname: MATH 1342 EXAM 2 REVIEW 30) ) ) ) Yes 34) ) ) ) $ ) $ ) ) ) ) ) ) ) Mean = 6.7, Variance = ) ) e ! 48)