Exam 4: Probability and Counting Rules

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Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. Let B be the event that exactly two doors are locked. List the outcomes of B Designate "locked" and U" designate "unlocked".]

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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?

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If the letters A, B, C, D, E, and F are to be used in a five-letter code, how many different codes are possible if repetitions are not permitted?

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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?

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A child gets 20 heads out of 30 tosses of a coin. If he declared the chance of getting a head with that coin were 2/3, that would be an example of probability.

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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?

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A package contains 10 resistors, 2 of which are defective. If 3 are selected, find the probability of getting 1 defective resistor.

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What is the set of all possible outcomes of a probability experiment?

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 If P(A)=0.38,P(B)=0.33, and P(A and B)=0.24, find P(A or B). \text { If } P ( A ) = 0.38 , P ( B ) = 0.33 \text {, and } P ( A \text { and } B ) = 0.24 \text {, find } P ( A \text { or } B ) \text {. }

(Multiple Choice)
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 Let A and B be events with P(A)=0.7,P(B)=0.3, and P(B∣A)=0.2. Find P(A and B). \text { Let } A \text { and } B \text { be events with } P ( A ) = 0.7 , P ( B ) = 0.3 \text {, and } P ( B \mid A ) = 0.2 \text {. Find } P ( A \text { and } B ) \text {. }

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When 3 dice are rolled, find the probability of getting a sum of 13.

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7P6 is equal to 7. { } _ { 7 } ^ { P } 6 \text { is equal to } 7 \text {. }

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If a sportscaster makes an educated guess as to how well a team will do this season, he is using what type of probability?

(Multiple Choice)
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On a recent Saturday, a total of 1086 people visited a local library. Of these people, 269 were under age 10, 466 were aged 10-18, 185 were aged 19-30, and the rest were more than 30 years old. One person is sampled at random. What is the probability that the person is more than 30 years Old?

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What is the correct relationship between events A and B: A: Karl is college graduate. B: Karl is a high school graduate.

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A fast-food restaurant chain has 633 outlets in the United States. The following table categorizes them by city population and location and presents the number of outlets in each category. An outlet is chosen at random from the 633 to test market a new menu. Region Population of city NE SE SW NW Under 50,000 28 30 31 22 50,000-500,000 58 46 54 42 Over 500,000 79 125 74 44 Given that the outlet is located in a city with a population under 50,000 , what is the probability that it is in the Southwest?

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FizzFizz soda comes in two varieties, regular and diet. If a researcher has 5 boxes of each, how many ways can he select 2 boxes of each for a quality control test?

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A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the Probability (as a reduced fraction) that both answers are the same ("AA", "BB" or "CC"). [Hint: List all the outcomes of the sample space first.]

(Multiple Choice)
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Let AA and BB be events with P(A)=0.9,P(B)=0.8P ( A ) = 0.9 , P ( B ) = 0.8 , and P(AP ( A and B)=0.36B ) = 0.36 . Are AA and BB mutually exclusive?

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If two dice are rolled one time, find the probability of getting a sum of 6.

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