4. Probability

80. Unusual Events Can any of the events in Exercises 75-78 be considered unusual? Explain.

81. Genetics A Punnett square is a diagram that shows all possible gene combinations in a cross of parents whose genes are known. When two pink snapdragon flowers (RW) are crossed, there are four equally likely possible outcomes for the genetic makeup of the offspring: red (RR), pink (RW), pink (WR), and white (WW), as shown in the Punnett square at the left. When two pink snapdragons are crossed, what is the probability that the offspring will be (c) white?

87. College Football A stem-and-leaf plot for the numbers of touchdowns allowed by the 127 NCAA Division I Football Bowl Subdivision teams in the 2020-2021 season is shown. Find the probability that a team chosen at random allowed (a) at least 51 touchdowns. Are any of these events unusual? Explain. (Source: National Collegiate Athletic Association)

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97. Rolling a Pair of Dice You roll a pair of six-sided dice and record the sum.

a. List all of the possible sums and determine the probability of rolling each sum.

b. Use technology to simulate rolling a pair of dice and record the sum 100 times. Make a tally of the 100 sums and use these results to list the probability of rolling

each sum.

c. Compare the probabilities in part (a) with the probabilities in part (b). Explain any similarities or differences.

In Exercises 1-4, identify the sample space of the probability experiment and determine the number of outcomes in the event. Draw a tree diagram when appropriate.

3. Experiment: Choosing a month of the year

Event: Choosing a month that begins with the letter J

In Exercises 7-12, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.

8. The probability of randomly selecting five cards of the same suit from a standard deck of 52 playing cards is about 0.002.

In Exercises 7-12, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.

11. The probability of rolling 2 six-sided dice and getting a sum of 9 is 1/9.

Using a Frequency Distribution to Find Probabilities In Exercises 49-52, use the frequency distribution at the left, which shows the population of the United States by age group, to find the probability that a U.S. resident chosen at random is in the age range. (Source: U.S. Census Bureau)

49. 18 to 24 years old

Using a Frequency Distribution to Find Probabilities In Exercises 49-52, use the frequency distribution at the left, which shows the population of the United States by age group, to find the probability that a U.S. resident chosen at random is in the age range. (Source: U.S. Census Bureau)

52. 65 years old and older

Classifying Types of Probability In Exercises 53-58, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.

55. An analyst feels that the probability of a team winning an upcoming game is 60%.

Classifying Types of Probability In Exercises 53-58, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.

58. You estimate that the probability of getting all the classes you want on your next schedule

is about 25%.

Marijuana Use The percent distribution of the last marijuana use (either medical or nonmedical) for a sample of 13,373 college students is shown in the pie chart. Find the

probability of each event. (Source: American College Health Association)

a. Randomly selecting a student who never used marijuana

88. Individual Stock Price An individual stock is selected at random from the portfolio represented by the box-and-whisker plot shown. Find the probability that the stock price is between \$21 and \$50.

Odds The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, when the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2 : 3 (read "2 to 3"). In Exercises 91-96, use this information about odds.

92. The probability of winning an instant prize game is 1/10. The odds of winning a different instant prize game are 1 : 10. You want the best chance of winning. Which game should you play? Explain your reasoning.

Odds The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, when the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2 : 3 (read "2 to 3"). In Exercises 91-96, use this information about odds.

94. A card is picked at random from a standard deck of 52 playing cards. Find the odds that it is a spade.