73.

Explain what is wrong with the following statements. Use complete sentences.

1. If there is a 60% chance of rain on Saturday and a 70% chance of rain on Sunday, then there is a 130% chance of rain over the weekend.
2. The probability that a baseball player hits a home run is greater than the probability that he gets a successful hit.

3.2Independent and Mutually Exclusive Events

Use the following information to answer the next 12 exercises.From January through December 2012, Gallup interviewed more than 170,000 employed Americans 18 years of age or order. The graph shown is compiled from data collected by Gallup. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score.

Figure3.18

74.

Find the probability that the selected Emotional Health Index Score is 82.7.

75.

Find the probability that the selected Emotional Health Index Score is 81.0.

76.

Find the probability that the selected Emotional Health Index Score is more than 81?

77.

Find the probability that the selected Emotional Health Index Score is between 80.5 and 82?

78.

If we know the selected Emotional Health Index Score is 81.5 or more, what is the probability that it is 82.7?

79.

What is the probability that the selected Emotional Health Index Score is 80.7 or 82.7?

80.

What is the probability that the selected Emotional Health Index Score is less than 80.2 given that it is already less than 81.

81.

What occupation has the highest emotional index score?

82.

What occupation has the lowest emotional index score?

83.

What is the range of the data?

84.

Compute the average EHIS.

85.

If all occupations are equally likely for a certain individual, what is the probability that he or she will have an occupation with lower than average EHIS?

3.3Two Basic Rules of Probability

86.

On February 28, 2013, a Field Poll Survey reported that 61% of California registered voters approved of allowing two people of the same gender to marry and have regular marriage laws apply to them. Among 18 to 39 year olds (California registered voters), the approval rating was 78%. Six in ten California registered voters said that the upcoming Supreme Court's ruling about the constitutionality of California's Proposition 8 was either very or somewhat important to them. Out of those CA registered voters who support same-sex marriage, 75% say the ruling is important to them.

In this problem, let:

• C= California registered voters who support same-sex marriage.
• B= California registered voters who say the Supreme Court's ruling about the constitutionality of California's Proposition 8 is very or somewhat important to them
• A= California registered voters who are 18 to 39 years old.

1. FindP(C).
2. FindP(B).
3. FindP(C|A).
4. FindP(B|C).
5. In words, what isC|A?
6. In words, what isB|C?
7. FindP(CB).
8. In words, what isCB?
9. FindP(CB).
10. AreCandBmutually exclusive events? Show why or why not.

87.

After Rob Ford, the mayor of Toronto, announced his plans to cut budget costs in late 2011, the Forum Research polled 1,046 people to measure the mayor's popularity. Everyone polled expressed either approval or disapproval. These are the results their poll produced:

• In early 2011, 60 percent of the population approved of Mayor Ford's actions in office.
• In mid-2011, 57 percent of the population approved of his actions.
• In late 2011, the percentage of popular approval was measured at 42 percent.

1. What is the sample size for this study?
2. What proportion in the poll disapproved of Mayor Ford, according to the results from late 2011?
3. How many people polled responded that they approved of Mayor Ford in late 2011?
4. What is the probability that a person supported Mayor Ford, based on the data collected in mid-2011?
5. What is the probability that a person supported Mayor Ford, based on the data collected in early 2011?

Use the following information to answer the next three exercises.The casino game, roulette, allows the gambler to bet on the probability of a ball, which spins in the roulette wheel, landing on a particular color, number, or range of numbers. The table used to place bets contains of 38 numbers, and each number is assigned to a color and a range.

Figure3.19(credit: film8ker/wikibooks)

88.

1. List the sample space of the 38 possible outcomes in roulette.
2. You bet on red. FindP(red).
3. You bet on -1st 12- (1st Dozen). FindP(-1st 12-).
4. You bet on an even number. FindP(even number).
5. Is getting an odd number the complement of getting an even number? Why?
6. Find two mutually exclusive events.
7. Are the events Even and 1st Dozen independent?

89.

Compute the probability of winning the following types of bets:

1. Betting on two lines that touch each other on the table as in 1-2-3-4-5-6
2. Betting on three numbers in a line, as in 1-2-3
3. Betting on one number
4. Betting on four numbers that touch each other to form a square, as in 10-11-13-14
5. Betting on two numbers that touch each other on the table, as in 10-11 or 10-13
6. Betting on 0-00-1-2-3
7. Betting on 0-1-2; or 0-00-2; or 00-2-3

90.

Compute the probability of winning the following types of bets:

1. Betting on a color
2. Betting on one of the dozen groups
3. Betting on the range of numbers from 1 to 18
4. Betting on the range of numbers 19-36
5. Betting on one of the columns
6. Betting on an even or odd number (excluding zero)

91.

Suppose that you have eight cards. Five are green and three are yellow. The five green cards are numbered 1, 2, 3, 4, and 5. The three yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card.

• G= card drawn is green
• E= card drawn is even-numbered
  1. List the sample space.
  2. P(G) = _____
  3. P(G|E) = _____
  4. P(GE) = _____
  5. P(GE) = _____
  6. AreGandEmutually exclusive? Justify your answer numerically.