Pitt MATH 1100 - Notes
Pages 36

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6.1An approach of assigning probabilities which assumes that all outcomes of the experiment are equally likely is referred to as the: CLASSICAL APPROACHIf A and B are mutually exclusive events with P(A) = 0.70, then P(B): CANNOT BE LARGER THAN .30If you roll a balanced die 50 times, you should expect an even number to appear: ALL OF THESE ARE TRUE (every other roll, exactly 50 times out of 100 rolls, 25 times on average-over the long term)The collection of all possible outcomes of an experiment is called: SAMPLE SPACEWhich of the following is an approach to assigning probabilities? RELATIVE FREQUENCY APPROACHA sample space of an experiment consists of the following outcomes: 1, 2, 3, 4, and 5. Which of the following is a simple event? 3Which of the following is a requirement of the probabilities assigned to outcome Oi? 0  P ( O i)  1 for each i If an experiment consists of five outcomes with P(O1) = 0.10, P(O2) = 0.20, P(O3) = 0.30, P(O4) = 0.15, then P(O5) is .25*Of the last 500 customers entering a supermarket, 50 have purchased a wireless phone. If the relative frequency approach for assigning probabilities is used, the probability that the next customer will purchase a wireless phone is .10If two events are collectively exhaustive, what is the probability that one or the other occurs? CANNOT BE DETERMINED FROM THE INFO.If two events are collectively exhaustive, what is the probability that both occur at the same time? CANNOT BE DETERMINED If two events are mutually exclusive, what is the probability that one or the other occurs? CANNOT BE DETMERMINEDIf two events are mutually exclusive, what is the probability that both occur at the same time? 0.00If two events are mutually exclusive and collectively exhaustive, what is the probability that both occur? 0.00If the two events are mutually exclusive and collectively exhaustive, what is the probability that oneor the other occurs? 1.00If events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs? CANNOT BE DETERMINED1*If two equally likely events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs? .50If event A and event B cannot occur at the same time, then A and B are said to be MUTUALLY EXCLUSIVEThe collection of all possible events is called A SAMPLE SPACE6.2Which of the following best describes the concept of marginal probability? It is a measure of the likelihood that a particular event will occur, regardless of whether another event occurs.The intersection of events A and B is the event that occurs when: BOTH A AND B OCCURThe probability of the intersection of two events A and B is denoted by P(A and B) and is called the JOINT PROBABILITYThe probability of event A gives event B is denoted by P ( A|B ) Which of the following is equivalent to P(A|B)? P ( A )/ P ( B ) **If two events are independent, what is the probability that they both occur? CANNOT BE DETERMINEDIf the outcome of event A is not affected by event B, then events A and B are said to be INDEPENDENT**If A and B are disjoint events with P(A) = 0.70, then P(B):cannot be larger than 0.30If P(A) = 0.65, P(B) = 0.58, and P(A and B) = 0.76, then P(A or B) is: 0.47Suppose P(A) = 0.50, P(B) = 0.75, and A and B are independent. The probability of the complement of the event (A and B) is: 1  (.5  .75) = .625 Which of the following statements is correct if the events A and B have nonzero probabilities? A and B cannot be both independent and disjoint A and B are disjoint events, with P(A) = 0.20 and P(B) = 0.30. Then P(A and B) is: 0.00If P(A) = 0.35, P(B) = 0.45, and P(A and B) = 0.25, then P(A|B) is: 0.556If A and B are independent events with P(A) = 0.60 and P(A|B) = 0.60, then P(B) is: CANNOT BE DETERMINEDIf A and B are independent events with P(A) = 0.20 and P(B) = 0.60, then P(A|B) is:0.202If P(A) = 0.25 and P(B) = 0.65, then P(A and B) is: CANNOT BE DETERMINEDSuppose X = the number of pets owned by a family in the U.S. The probability distribution of X is shown in the table below.X 0 1 2 3Probability 0.56 0.23 0.12 0.09Pets Narrative} What is the chance that a family owns more than one pet? 0.21{Pets Narrative} Suppose you choose two families at random. What is the chance that they each own one pet? (That means family A owns a pet and family B owns a pet.)(0.23)*(0.23) = 0.05296.3If P(A) = 0.84, P(B) = 0.76, and P(A or B) = 0.90, then P(A and B) is:0.70If P(A) = 0.20, P(B) = 0.30, and P(A and B) = 0, then A and B are:mutually exclusive eventsIf P(A) = 0.65, P(B) = 0.58, and P(A and B) = 0.76, then P(A or B) is: 0.47Suppose P(A) = 0.35. The probability of the complement of A is:0.65If the events A and B are independent with P(A) = 0.30 and P(B) = 0.40, then the probability that both events will occur simultaneously is:0.12If events A and B are independent then:P ( A and B ) = P ( A ) * P ( B ) Two events A and B are said to be mutually exclusive if:P ( A and B ) = 0 Which of the following statements is always correct?P ( A ) = 1  P ( A c ) If A and B are mutually exclusive events, with P(A) = 0.20 and P(B) = 0.30, then the probability that both events will occur simultaneously is: 0If A and B are independent events with P(A) = 0.60 and P(B) = 0.70, then P(A or B) equals:0.88If A and B are mutually exclusive events with P(A) = 0.30 and P(B) = 0.40, then P(A or B) is:0.70If A and B are any two events with P(A) = .8 and P(B|A) = .4, then P(A and B) is:.323If A and B are any two events with P(A) = .8 and P(B|Ac) = .7, then P(Ac and B) is.326.4/6.5 Bayes Law and prior posterior probabilitiesA posterior probability value is a prior probability value that has been:modified on the basis of new information.Which of the following statements is false?There is no formula defining Bayes' Law.Which of the following statements is false regarding a scenario using Bayes' Law?Prior probabilities are called likelihood probabilities.Bayes' Law is used to compute:posterior probabilities.Initial estimates of the probabilities of events are known as:prior probabilities7.1The weighted average of the possible values that a random variable X can assume, where the weights are the probabilities of occurrence of those values, is referred to as the:expected value.The number of accidents that occur annually on a busy stretch of highway is an

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# Pitt MATH 1100 - Notes

Pages: 36
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