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Chapter 5: Q 16. (page 247)
If you sum the probabilities of the possible values of a discrete random variable, the result always equals .
If you sum the probabilities of the possible values of a discrete random variable, the result always equalsto 1.
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World Series. The World Series in baseball is won by the first team to win four games (ignoring the 1903 and 1919鈥�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?
Interpret each of the following probability statements, using the frequentist interpretation of probability.
(a). The probability is 0.487 that a newborn baby will be a girl.
(b). The probability of a single ticket winning a prize in the Powerball lottery is 0.031.
Give two examples of Bernoulli trials other than those presented in the text.
Suppose that a simple random sample is taken from a finite population in which each member is classified as either having or not having a specified attribute. Fill in the following blanks.
(a) If sampling is with replacement, the probability distribution of the number of members sampled that have the specified attribute is a distribution.
(b) If sampling is without replacement, the probability distribution of the number of members sampled that have the specified attribute is a distribution.
(c) If sampling is without replacement and the sample size does not exceed % of the population size, the probability distribution of the number of members sampled that have the specified attribute can be approximated by a distribution.
An ordinary deck of playing cards has 52 cards. Three are four suits_ spade heart , diamond and club with 13 card in each suit. Spade and clubs are black heart and diamond are red. One of these cards is selected at random. Let R denote the event that a red is chosen . Find the probability that a red card is chosen, and express your answer in probability that a red card is chosen and express your answer in probability natation
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