Math 120 Practice Exam II Name You must show work for credit. 1) A pair of fair dice is rolled 50 times and the sum of the dots on the faces is noted. Outcome 2 4 5 6 7 8 9 10 11 12 Frequency 6 8 8 1 5 9 7 0 0 Compute the empirical probability that the sum rolled is greater than 9. 1) Estimate the indicated probability. 2) The Amboy Kennel Club has held an annual dog show for the last 0 years. During this time the winner of ʺBest of Showʺ has been an Alaskan Malamute 15 times, a Great Pyrenees times, and an Siberian Husky 12 times. Determine the empirical probability that the next winner of ʺBest of Showʺ will be an Alaskan Malamute. 2) ) A survey was done at a mall in which 1000 customers were asked what type of credit card they used most often. The results of the survey are shown in the figure below: ) 0.2% 7.8% 1.2% 2.5% 16.% Determine the empirical probability that a person selected at random from the 1000 surveyed uses Mastercard. 4) Determine the probability that the spinner lands on white. 4) 5) If a person is randomly selected, find the probability that his or her birthday is in May. Ignore leap years. Assume that all days of the year are equally likely for a given birth. 5) 1
6) When two balanced dice are rolled, there are 6 possible outcomes. Find the probability that either doubles are rolled or the sum of the dice is 8. 6) 7) A card is drawn at random from a standard 52 -card deck. Find the probability that the card is an ace or not a club. 7) Find the odds. 8) 8) What are the odds in favor of drawing an even number from these cards? 9) The odds in favor of Carl beating his friend in a round of golf are 7 :. Find the probability that Carl will lose. 9) 10) If it has been determined that the probability of an earthquake occurring on a certain day in a certain area is 0.01, what are the odds in favor of an earthquake? 10) 11) Numbers is a game where you bet $1.00 on any three -digit number from 000 to 999. If your number comes up, you get $600.00. Find the expected winnings. 11) 12) Experience shows that a ski lodge will be full (181 guests) if there is a heavy snow fall in December, while only partially full (88 guests) with a light snow fall. What is the expected number of guests if the probability for a heavy snow fall is.40? 12) 1) An insurance company will insure a $260,000 home for its total value for an annual premium of $590. If the company spends $0 per year to service such a policy, the probability of total loss for such a home in a given year is 0.001 and you assume either total loss or no loss will occur, what is the companyʹs expected annual gain (or profit) on each such policy? 1) 14) Assume that a person spins the pointer and is awarded the amount indicated if the pointer points to a positive number but must pay the amount indicated if the pointer points to a negative number. Determine the personʹs expectation. 14) $9 -$7 $1 2
Use the counting principle to obtain the answer. 15) A saleswoman packed jackets and 6 skirts. With one jacket, she could wear all 6 skirts. With another jacket, she could wear 5 skirts. With the third jacket, she could wear only 2 skirts. How many different combinations did she have? 15) 16) A couple plans to have four children. Using a tree diagram, obtain the sample space. List the elements that make up the sample space. (Use ʺBʺ for ʺboyʺ and ʺGʺ for ʺgirl.ʺ) 16) 17) There are cards in a hat; one is a king, one is a queen, and one is an ace. Two cards are to be selected at random with replacement. Using a tree diagram, obtain the sample space for the experiment. Then, find the probability that a king and a queen are selected. 17) Find the indicated probability. 18) If P(A) = 0.2, P(A or B) = 0.5, and P(A and B) = 0., find P(B). 18) 19) Each of ten tickets is marked with a different number from 1 to 10 and put in a box. If you draw a ticket from the box, what is the probability that you will draw 2, 5, or 1? 19) 20) The odds in favor of Trudy beating her friend in a round of golf are 1 : 9. Find the probability that Trudy will lose. 20) Find the odds. 21) A number cube labeled with numbers 1, 2,, 4, 5, and 6 is tossed. What are the odds in favor of the cube showing a number less than? 21) 22) The chart below gives the number of vehicle tags sold in each city. 22) City Number of Vehicle Tags Sold Bristol 1,86 Trevor 507 Camp Lake 2,457 Salem 177 Paddock Lake 2,541 One car is selected at random from the cars with vehicle tags from these cities. What is the probability that this car is from Salem? (Round your answer to four decimal places.) 2) A spinner has regions numbered 1 through 21. What is the probability that the spinner will stop on an even number or a multiple of? 2) 24) One card is selected from a deck of cards. Find the probability of selecting a red card or a heart. 24)
25) If you are dealt two cards successively (with replacement of the first) from a standard 52-card deck, find the probability of getting a face card on the first card and an ace on the second. 25) 26) An IRS auditor randomly selects tax returns (without replacement) from 47 returns of which 5 contain errors. What is the probability that she selects none of those containing errors? 26) 27) If two cards are drawn without replacement from a deck, find the probability that the second card is a spade, given that the first card was a spade. 27) Two marbles are drawn without replacement from a box with white, 2 green, 2 red, and 1 blue marble. Find the probability. 28) The second marble is blue given the first marble is blue. 28) Use the table to find the probability. 29) The following table indicates the preference for different types of soft drinks by three age groups. cola root beer lemon-lime under 21 years of age 40 25 20 between 21 and 40 5 20 0 over 40 years of age 20 0 5 If a person is selected at random, find the probability that the person is over 40 years of age given that they drink root beer. 29) 0) A baseball manager has 12 players of the same ability. How many 9 player starting lineups can he create? 0) An order of award presentations has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia, and Paul. 1) In how many ways can the men be presented first and then the women? 1) Suppose a traveler wanted to visit a museum, an art gallery, and the state capitol building. 45 -minute tours are offered at each attraction hourly from 10 a.m. through p.m. (6 different hours). Solve the problem, disregarding travel time. 2) In how many ways could the traveler schedule all three tours before 1 p.m.? 2) ) A license plate is to consist of 2 letters followed by digits. Determine the number of different license plates possible if repetition of letters and numbers is not permitted. ) Evaluate the expression. 4) 7C 4 7 P 4 4) 4
5) In how many ways can a group of 9 students be selected from 10 students? 5) 6) How many 5-card poker hands consisting of aces and 2 kings are possible with an ordinary 52-card deck? 6) 7) A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if the committee can have at most two girls? 7) Find the probability (as a decimal rounded to four decimal places). 8) A bag contains 6 cherry, orange, and 2 lemon candies. You reach in and take pieces of candy at random. Find the probability that you have one candy of each flavor. 8) 9) A bag contains 6 cherry, orange, and 2 lemon candies. You reach in and take pieces of candy at random. What is the probability that you have at least 2 cherry candies? 9) Find the probability of the following five-card poker hands from a 52-card deck. In poker, aces are either high or low. 40) Four of a kind (4 cards of the same value) 40) Assume that each of the n trials is independent and that p is the probability of success on a given trial. Use the binomial probability formula to find P(x). Round to four decimal places. 41) n = 11, x = 9, p = 0.4 41) 42) A family has five children. The probability of having a girl is 1/2. What is the probability of having at least boys? 42) 4) A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly four fives? 4) 44) A coin is biased to show 41% heads and 59% tails. The coin is tossed twice. What is the probability that the coin turns up heads once and tails once? 44) 45) In a certain college, % of the physics majors are ethnic minorities. A random sample of 10 physics majors is chosen. Find the probability that no more than 6 are ethnic minorities. 45) 5
Answer Key Testname: MATH 120 PRACTICE EXAM 2 F08 1) 7 50 2) 1 2 ) 0.78 4) 1 4 5) 1 65 5 6) 18 7) 10 1 8) 2: 9) 10 10) 1 to 99 11) -$0.40 12) 125.2 1) $00 14) -$1 15) 1 16) BBBB, BBBG, BBGB, BBGG, BGBB, BGBG, BGGB, BGGG, GBBB, GBBG, GBGB, GBGG, GGBB, GGBG, GGGB, GGGG 17) 2 9 18) P(B) = 0.6 19) 10 9 20) 10 21) 1:2 22) 0.1460 2) 2 24) 1 2 25) 169 26) 0.708 4 27) 17 28) 0 29) 2 5 0) 79,8,600 1) 144 6
Answer Key Testname: MATH 120 PRACTICE EXAM 2 F08 2) 6 ) 468,000 1 4) 24 5) 10 6) 24 7) 4620 8) 0.2182 9) 0.5758 1 40) 4165 41) 0.0052 42) 0.5000 4) 0.0080 44) 0.488 45) 0.9815 7