Identifying Simple Events In Exercises 33-36, determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning.

34. A spreadsheet is used to randomly generate a number from 1 to 4000. Event B is generating a number less than 500.

Using the Fundamental Counting Principle In Exercises 37-40, use the Fundamental Counting Principle.

37. Menu A restaurant offers a $15 dinner special that lets you choose from 6 appetizers, 12 entrées, and 8 desserts. How many different meals are available when you select an appetizer, an entrée, and a dessert?

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.

Boy or Girl? In Exercises 71-74, a couple plans to have three children. Each child is equally likely to be a boy or a girl.

74. What is the probability that at least one child is a boy?

Identifying the Sample Space of a Probability Experiment In Exercises 25-32, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriate.

31. Rolling a pair of six-sided dice

"Identifying the Sample Space of a Probability Experiment In Exercises 25-32, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriate.

26. Guessing a student's letter grade (A, B, C, D, F) in a class

"

True or False? In Exercises 3-6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

3. A combination is an ordered arrangement of objects.

True or False? In Exercises 7-10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

9. A probability of 1/10 indicates an unusual event.

Cards In Exercises 59-62, you are dealt a hand of five cards from a standard deck of 52 playing cards.

59. Find the probability of being dealt two clubs and one of each of the other three suits.

Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

20. Coin and Die A coin is tossed and a die is rolled. Find the probability of tossing a tail and then rolling a number greater than 2.

Finding the Probability of an Event In Exercises 21-24, the probability that an event will not happen is given. Find the probability that the event will happen. 

23. P(E')=3/4

Matching Probabilities In Exercises 11-16, match the event with its probability.

a. 0.95

b. 0.005

c. 0.25

d. 0

e. 0.375

f. 0.5

14. A game show contestant must randomly select a door. One door doubles her money while the other three doors leave her with no winnings. What is the probability she selects the

door that doubles her money?

"According to Bayes’ Theorem, the probability of event A , given that event B has occurred, is

P(A|B) = P(A) * P(B|A)P(A) * P(B|A) + P(A') * P(B|A').

In Exercises 33–38, use Bayes’ Theorem to find P(A|B).

36. P(A) = 0.62, P(A') = 0.38, P(B|A) = 0.41 , and P(B|A') = 0.17 "

Finding Classical Probabilities In Exercises 41-46, a probability experiment consists of rolling a 12-sided die numbered 1 to 12. Find the probability of the event.

43. Event C: rolling a number greater than 4

In Exercises 15-18, determine whether the situation involves permutations, combinations, or neither. Explain your reasoning.

17. The number of ways 2 captains can be chosen from 28 players on a lacrosse team

Using a Pie Chart to Find Probabilities In Exercises 83-86, use the pie chart at the left, which shows the number of workers (in millions) by occupation for the United States. (Source: U.S. Bureau of Labor Statistics)

84. Find the probability that a worker chosen at random is not employed in a service occupation.

31. Experiment A researcher is randomly selecting a treatment group of 10 human subjects from a group of 20 people taking part in an experiment. In how many different ways can the treatment group be selected?

Using a Bar Graph to Find Probabilities In Exercises 75-78, use the bar graph at the left, which shows the highest level of education received by employees of a company. Find the probability that the highest level of education for an employee chosen at random is

77. a master's degree.

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

Classifying Events as Independent or Dependent In Exercises 9-14, determine whether the events are independent or dependent. Explain your reasoning.

11. Returning a rented movie after the due date and receiving a late fee

According to Bayes’ Theorem, the probability of event A , given that event B has occurred, is

P(A|B) = P(A) * P(B|A)P(A) * P(B|A) + P(A') * P(B|A').

In Exercises 33–38, use Bayes’ Theorem to find P(A|B).

33. P(A) = 2/3, P(A') = 1/3, P(B|A) = 1/5 , and P(B|A') = 1/2

"Classifying Events as Independent or Dependent In Exercises 9-14, determine whether the events are independent or dependent. Explain your reasoning.

12. Not putting money in a parking meter and getting a parking ticket"

34. Lottery Number Selection A lottery has 52 numbers. In how many different ways can six of the numbers be selected? (Assume the order of selection is not important.)

"Classifying Events Based on Studies In Exercises 15-18, identify the two events described in the study. Do the results indicate that the events are independent or dependent? Explain your reasoning.

15. A study was conducted to debunk the idea that abilities in music and math are related. Instead, the study showed a strong relationship between achievements in music and math.

(Source: University of Kansas)"

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%.

Recognizing Mutually Exclusive Events In Exercises 9–12, determine whether the events are mutually exclusive. Explain your reasoning.

10. Event A: Randomly select a student with a birthday in April.

Event B: Randomly select a student with a birthday in May.

28. Necklaces You are putting nine blue glass beads, three red glass beads, and seven green glass beads on a necklace. In how many distinguishable ways can the colored beads be put on the necklace?

"Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

22.Pickup Trucks In a survey, 510 U.S. adults were asked whether they drive a pickup truck and whether they drive a Ford. The results showed that three in twenty adults surveyed drive a Ford. Of the adults surveyed that drive Fords, nine in twenty drive a pickup truck. Find the probability that a randomly selected adult drives a Ford and drives a pickup truck.

True or False? In Exercises 5 and 6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

6. If events A and B are dependent, then P(A and B) = P(A) · P(B).

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.