hw3 - Identify the sample space of the probability...

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Unformatted text preview: Identify the sample space of the probability experiment. Picking a random nutnber from 1 to 5 Choose the correct sample space. 0 a. {o, 1, 2, 3, 4, 5} 0 by {11,12,13,14,15, 22, 23, 24, 25, 33, 34, 35, 44, 45, 55} 00- {1.2.14.5} The sample space is the set ofall possible outcomes of'a probability experiment. Classify the statement as an example of classical probability, empirical probability, or subjective probability. The probability that a varsity basketball player will miss a free throw is 11"3 Choose the type of probability. 0 3- Classical probability 0 1;, Empirical probability 0 C. Subjective probability Classical probability is used when each outcome in a sample space is equally likely to occur. Empirical probability is based on observations obtained from probability experiments. Subjective probabilities result from intuition, educated guesses, and estimates. Consider a company that selects employees for random drug tests. The company uses a computer to select randomly employee numbers that range from 1 to T466 Find the probability of selecting a number less than SUD. Probability of selecting a number less than SUD = I107" (Round to the nearest hundredth.) The event of selecting a number less than SUD has 499 outcomes. Number of outcomes in E USE the formula FIE) = Total number of outcomes in sample space ' The Venn diagram displays the results ofall of the registered voters in a county. Wfifhat is the probability that a registered voter in the county voted in the election? P(voter voted) = (Round to four decimal places.) Find the total number of registered voters in the county by adding together those that voted and those who did not vote. Then use the formula. Number of outcomes in E FEE) _ Total number of outcomes in sample space ’ where E is the number of registered voters who voted. The odds of Winning is the ratio ofthe number of successful outcomes to the number of unsuccessful outcomes. The odds oflosing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, if the number of successful outcomes is 2 and the number ofunsuccessful outcomes is 6, the odds ofa success are 2:6, or in reduced form 1:3. A card is picked at random from a standard deck of 52 playing cards. Find the odds that the card is a black card. Odds that the card is a black card= |:| : |:| (Simplify your answer. Type integers.) There are 26 black cards in a deck of 52 playing cards. Odds = Number of successful outcomes : Number of unsuccessful outcomes, where a successful outcome is drawing a black card and an unsuccessful outcome is not drawing a black card. The table shows the results ofa survey in which 16? families were asked if they own a home and if they will be purchasing a new vehicle this ymr Buying a New Car This Year '.y is buying a new car this year given that they Find the probability that a randomly selected fanny is buying a new car this year and owns a home. D. 305 (Round to the nearest thousandth.) To find the conditional probability, find the nurnber of farnilies that meet both conditions, those that ovv‘n a home and will be buying a new car this year, and divide by the number of families in the sample space that meet the given condition, the total nurnber Elf fainilies that own a home. To find the probability, find the number of families that meet both conditions, those that ovtm a home and ‘will be buying a new car this year, and divide by the total number of families in the sample space. In a survey, 40% of students at a state university live in on—carnpus housing. Of these 40%, 2 out of 10 said that on—cainpus housing is too expensive. Find the probability that a randomly selected student lives in on—carnpus housing and thinks that on—carnpus housing is too expensive. DDS Given that a randomly selected student lives in on— campus housing, find the probability that he or she does not think that on—carnpus housing is too expensive. El Use the Multiplication Rule, PU—‘t and B) = HA) - HEM), where A is the event that a student lives in on—campus housing and B is the event that a student thinks on—campus housing is too expensive. You know that 2 out of ID said that on—carnpus housing is too expensive. How many think that on—carnpus house is NOT too expensive? Use this proportion to find the probability that an on—carnpus person does not think housing is too expensive. A statistics professor was born on November 20. TWhat is the probability that 3 of her students randomly selected were born on November 20'? Assume 365 days in a year. Choose the correct probability. 0 a. oooooo'i45514 Db. ooooooi‘som 0c. Il.EIEIE?39?2fi D d. oooooooozoso To find the probability, use the fact that a person's birthday is independent from another person's birthday. Then since they are independent events, you can use the Multiplication Rule to find the probability. According to Bayes' Theorem, the probability of event A, given that event E- has occurred, is PEAJ'PEBIA] PEAIBJ— PEAi].p[B|A*]+P[E-IA]'P[AJ Use Bayes' Theorem to find P(A|Eu). P(A) = £1.23, PfiA') = on, maps) = o. 1, and mat-5:) = no P(A|Eu) = 0.0321 (Round to four decimal places.) Make sure you are using the formula correctly. The values are given; place them in the formula and solve. _ PEAl'PEBIA] o.23-o.1 ‘ P[A']-P[E|A“]+P[E|A]'P[A] _ EI.7?-EI.9+IZI.1-D.23 PEAIB] A certain virus infects one in every 400 people. A test us ed to detect the virus in a person is positive T8% of the time if the person has the virus and 3% of the time if the person does not have the virus. (This 3% is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive. " Find the probability, given a person tests positive, that the person really is infected. If a person tests positive, what is the probability that the person is infected? (Round to four decimal places.) The events are dependent. Use the Multiplication Rule and Bayes' Theorem. PEA] ' PEEIA] PEAIE-J— Hairpmlgenpmrpmlm College Students Decide if the events shown in the Venn diagram are mutually exclusive. Choose the correct statement. 3' El- The events are not mutually exclusive. 0 '0- The events are mutually exclusive. The events are not mutually exclusive. Mutually exclusive events are events that cannot occur at the same time. In a sample of 2200 people, 17"0 have brown hair. Two unrelated people are selected at random from the sample. Find the following probabilities. P(both people have brown hair) = [.006 (Round to the nearest thousandth.) P(neither person has brown hair) = 0. 851 (Round to the nearest thousandth.) P(at least one ofthe people has brown hair) = 0.149 (Round to the nearest thousandth.) Evaluate 13(1). and B] = 13(2).) ' PEBIA] , where A and B are dependent events. Evaluate PEA and B] = PEA] ' PEBIA] , where A and B are dependent events. Recall that the probability of ”at least one" event occurring is the complement of the probability of "none of" the events occurring. P[at least one person has brown hair] = 1 — P[neither person has brown hair] The Addition Rule for the probability that events A or B or C will occur P(A or B or C) is given by P(A or a or C) = P(A) + 1303) + 13(0) — P(A and a) — Pm and C) — P(B and C) + Pm and a and C) In the Venn diagram at the right, P(A or B or C) is given by the light blue areas. Find P(A or B or C) for the given probabilities. P(A) = 0.36, 13(3) = 0.36, P(C) = 0.28 P(A and B) = 0.16, P(A and C) = 0.26, P(B and C) = 0.1? P(A andB and C) = 0.14 P(A or B or C) = 0.55 (Round to the nearest hundredth.) All of the values are given to you. Substitute them in the given equation and evaluate. Perform the indicated calculation. 12! 12!=— Determinetheproductl2-ll-10- - 1. (Type an Integer) alternatively, use the factorial function on a calculator. Perform the indicated calculation. laps 13135 =1023160 (Typ e an integer.) A pizza menu has five choices for meat toppings, six choices for cheese toppings, and eight choices for vegetable toppings. How many different pizza combinations are available if you select one meat topping, one cheese topping, and one vegetable topping? different pizza combinations are available. (Type an integer.) In how many ways can the numbers 3, 4, 5, 6, and 7", be arranged, without repetition, for a five—digit identification number? different five-digit numbers can be made. (Type an integer.) Use the Fundamental Counting Principle. In a state lottery, you must select 6 numbers (in any order) out of 50 correctly to win the top prize. How many ways can 6 numbers be chosen from 50 numbers? ISBSIIJTEIIJ (Type an integer.) You purchase one lottery ticket. What is the probability of wiming the top prize? 000000006 (Round to 3 decimal places.) Evaluate so Ce . :1! Use the formula r: cr- = In a state lottery, you must select 6 numbers (in any order) out of 55 correctly to win the top prize. How many ways can 6 numbers be chosen from 55 numbers? 28989675 (Type an integer.) You purchase one lottery ticket. What is the probability of winning the top prize? 0. 00000003 (Round to 8 decimal places.) Evaluate 55 C6 . n ! Usethe formula ”Cr: —. (n—J'JIJ'! In a state lottery, you must select 6 numbers (in any order) out of 52 correctly to win the top prize. How many ways can 6 numbers be chosen from 52 numbers? (Type an integer.) Evaluate 52 Ce . You purchase one lottery ticket. fifhat is the probability of winning the top prize? D-DDDDDDDS Use the formula nCr= —. (Round to 8 decimal places.) (I: — r] ! r! n ! ...
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