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Chapter 5: Q 5.8. (page 216)
Suppose that C and D are mutually exclusive events such that and Determine .
As a result, has a value of
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Discuss the pros and cons of binomial probability tables.
Constract a venn diagram representing the event.
Part (a) (A (not B)).
Part (b) ((A or B) & (not(A & B)))
Vitamin C and Aspirin A bottle contains a label stating that it contains Spring Valley pills with 500 mg of vitamin C, and another bottle contains a label stating that it contains Bayer pills with 325 mg of aspirin. When testing claims about the mean contents of the pills, which would have more serious implications: rejection of the Spring Valley vitamin C claim or rejection of the Bayer aspirin claim? Is it wise to use the same significance level for hypothesis tests about the mean amount of vitamin C and the mean amount of aspirin?
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?
In Exercises 5.16-5.26, express your probability answers as a decimal rounded to three places.
Preeclampsia. Preeclampsia is a medical condition characterized by high blood pressure and protein in the urine of a pregnant woman. It is a serious condition that can be life-threatening to the mother and child. In the article "Women's Experiences Preeclampsia: Australian Action on Preeclampsia Survey of Wom and Their Confidants" (Journal of Pregnancy,Vol. 2011, Issue 1, Article ID 375653), C. East et al. examined the experiences of 68 women with preeclampsia. The following table provides a frequency distribution of instances of prenatal or infant death for infants of women with preeclampsia.
Suppose that one of these women with preeclampsia is randomly selected. Find the probability that the child of the woman selected
(a) died.
(b). died one week to six months after birth.
(c). lived at least six weeks.
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