Chapter 5: Q 5.45. (page 209)
Constract a venn diagram representing the event.
Part (a) (A (not B)).
Part (b) ((A or B) & (not(A & B)))
Short Answer
Part (a) (A (not B)).

Part (b) ((A or B) & (not(A & B)))

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Chapter 5: Q 5.45. (page 209)
Constract a venn diagram representing the event.
Part (a) (A (not B)).
Part (b) ((A or B) & (not(A & B)))
Part (a) (A (not B)).

Part (b) ((A or B) & (not(A & B)))

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In 10 Bernoulli trials, how many outcomes contain exactly three successes?
Roughly speaking, What is an experiment? an event?
Equipment breakdowns: A factory manager collected data on the number of equipment breakdown per day. From those data she derived the probability distribution shown in the following table, Where W denote the number of breakdown on a given day.

Part (a) Determine , Round your answer for the standard deviation to three decimal places.
Part (b) On average, how many breakdown occur per day?
Part (c) About how many breakdown are expected during a 1 year period assuming 250 work days per year?
Expected Utility. One method for deciding among various investment involves the concept of expected utility. Economists describe the importance of various levels of wealth by using utility functions. For instance, in most case, a single dollar is more important (has greater utility ) for someone with little wealth than for someone with greater wealth Consider two investments, say investment A and B. Measured in thousand of dollars, suppose that investment A yields 0, 1, and 4 with probability 0.1 and16 with probability 0.5, 0.3 and 0.2 respectively. Let Y denote the yield of an investment. For the two investment, determine and compare.
Part (a) The mean of Y, the expected yield.
Part (b) The mean of ,the expected utility, using the utility function role="math" localid="1651845051902" Interpret the utility function
Part (c) The mean of ,the expected utility, using the utility function . Interpret the utility function v
World Series. The World Series in baseball is won by the first team to win four games (ignoring the 1903 and 1919–1921 World Series, when it was a best of nine). Thus it takes at least four games and no more than seven games to establish a winner. From the document World Series History on the Baseball Almanac website, as of November 2013, the lengths of the World Series are as given in the following table
| Number of Games | Frequency | Relative Frequency |
| 4 | 21 | 0.200 |
| 5 | 24 | 0.229 |
| 6 | 24 | 0.229 |
| 7 | 36 | 0.343 |
a. If X denotes the number of games that it takes to complete a World Series, identify the possible values of the random variable X.
b. Do the first and third columns of the table provide a probability distribution for X? Explain your answer.
c. Historically, what is the most likely number of games it takes to complete a series?
d. Historically, for a randomly chosen series, what is the probability that it ends in five games?
e. Historically, for a randomly chosen series, what is the probability that it ends in five or more games?
f. The data in the table exhibit a statistical oddity. If the two teams in a series are evenly matched and one team is ahead three games to two, either team has the same chance of winning game number six. Thus there should be about an equal number of six-and seven-game series. If the teams are not evenly matched, the series should tend to be shorter, ending in six or fewer games, not seven games. Can you explain why the series tend to last longer than expected?
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