Lesson_3-_Probabilities_Workbook_F12SpaceUpdated

Brown or collins wins problem

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Unformatted text preview: uters Sold Probability 0 .08 1 .17 2 .26 3 .21 4 .18 5 .10 a. If we define the experiment as observing the number of computers sold tomorrow, determine the sample space. b. Use set notation to define the event, sell more than 3 computers. c. What is the probability of selling 5 computers? d. What is the probability of selling 2, 3, or 4 computers? e. What is the probability of selling 6 computers? Problem # 3.10 Two marbles are drawn at random and without replacement from a box containing two blue marbles and three red marbles. a. List the sample points for this experiment b. Assign probabilities to the sample points c. Determining the probability of observing each of the following events: A: {two blue marbles are drawn} B: {A red and a blue marble are drawn} C: {two red marbles are drawn} Problem # 3.11 If there are 30 red and blue marbles in a jar, and the ratio of red to blue marbles is 2:3, what is the probability that, drawing twice, you will select two red marbles if you return the marbles after each draw? 3 Problem # 3.12 Survey on energy conservation. A state energy agency mailed questionnaires on energy conservation to 1,000 homeowners in the state capital. Five hundred questionnaires were returned. Suppose an experiment consists of randomly selecting and reviewing one of the returned questionnaires. Consider the events: A: {The home is constructed of brick} B: {The home is more than 30 years old} C: {The home is heated with oil} Describe each of the following events in terms of unions, intersections and complements (ie., A U B, A∩ B, Ac , etc.): a. b. c. d. The home is more than 30 years old and is heated with oil. The home is not constructed of brick The home is heated with oil or is more than 30 years old. The home is constructed of brick and is not heated with oil. Problem # 3.13 Draw the Venn diagram where P(E1) = .10, P(E2) = .05, P(E3) = P(E4) = .2, P(E5) = .06, P(E6) = .3, P(E7) =.06 and P(E8) =.03. Find the following probabilities: a. P(Ac) = b. P(Bc) = c. P(Ac ∩ B) = d. P(A ∪ B) = e. P(A ∩ B) = f. P(Ac ∩ Bc) = g. Are events A and B mutually exclusive? Why? Problem # 3.14 Given that P(A∩B) =.4 and P(A|B) = .8, find P(B) 4 Problem # 3.15 Suppose we have the following joint probabilities. Compute the marginal probabilities A1 A2 A3 B1 .15 .20 .10 B2 .25 .25 .05 Problem # 3.16 a. Compute P(A2|B2 ) b. Compute P(B2|A2 ) c. Compute P(B1|A2 ) Proble...
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