4. Probability

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

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

23. Celebrities as Role Models In a sample of 1103 probable voters, three out of four say they would like entertainers to address social and political issues. Two probable voters are selected at random. (Source: The Hollywood Reporter)

a. Find the probability that both probable voters would like entertainers to address social and political issues.

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

29. In Vitro Fertilization In a recent year, about 1.9% of all infants born in the U.S. were conceived through assisted reproductive technology (ART). Of the ART deliveries, about 26.4% resulted in multiple births. (Source: Morbidity and Mortality Weekly Report)

a. Find the probability that a randomly selected infant was conceived through ART and was part of a multiple birth.

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

30. Standardized Test Scores According to a survey, 57.8% of college-seeking high school seniors say they have taken one of the standardized tests for potential college students. Of these, 35.6% say they do not plan to submit their score with their college applications. (Adapted from Niche)

b. Find the probability that a randomly selected college-seeking high school senior took one of the standardized tests and plans to submit this score with their college

applications.

4. Determine whether the events are mutually exclusive. Then determine whether the events are independent or dependent. Explain your reasoning.

Event A: A bowler having the highest game in a 40-game tournament

Event B: Losing the bowling tournament

In Exercises 19-22, determine whether the events are independent or dependent. Explain your reasoning.

22. Getting high grades and being awarded an academic scholarship

High School Dropouts According to the U.S. Census Bureau, 8.0% of 16- to 24-year-olds are high school dropouts. In addition, 2.1% of 16- to 24-year-olds are high school dropouts and unemployed. What is the probability that a randomly selected 16- to 24-year-old is unemployed, given he or she is a dropout?

[NW] Acceptance Sampling Suppose that you just received a shipment of six televisions and two are defective. If two televisions are randomly selected, compute the probability that both televisions work. What is the probability that at least one does not work?

"Playing Music on Random Setting

Suppose that a Spotify playlist has 13 tracks. After listening to all the songs, you decide that you like 5 of them. With the random feature on the playlist, each of the 13 songs is played once in random order. Find the probability that among the first two songs played:

b. You like neither of them."

"Planting Tulips

A bag of 30 tulip bulbs purchased from a nursery contains 12 red tulip bulbs, 10 yellow tulip bulbs, and 8 purple tulip bulbs. Use a tree diagram like the one in Example 5 to answer the following:

c. What is the probability that the first bulb selected is yellow and the second is red?

"

"Golf Balls

The local golf store sells an “onion bag” that contains 35 “experienced” golf balls. Suppose that the bag contains 20 Titleists, 8 Maxflis, and 7 Top Flites. Use a tree diagram like the one in Example 5 to answer the following:

b. What is the probability that the first ball selected is a Titleist and the second is a Maxfli?"

"A Flush

A flush in the card game of poker occurs if a player gets five cards that are all the same suit (clubs, diamonds, hearts, or spades). Answer the following questions to obtain the probability of being dealt a flush in five cards.

c. A royal flush in the game of poker occurs if the player gets the cards Ten, Jack, Queen, King, and Ace all in the same suit. Use the procedure given in parts (a) and (b) to compute the probability of being dealt a royal flush."

Mega Millions In Mega Millions, an urn contains balls numbered 1–56, and a second urn contains balls numbered 1–46. From the first urn, 5 balls are chosen randomly, without replacement and without regard to order. From the second urn, 1 ball is chosen randomly. For a \$1 bet, a player chooses one set of five numbers to match the balls selected from the first urn and one number to match the ball selected from the second urn. To win, all six numbers must match; that is, the player must match the first 5 balls selected from the first urn and the single ball selected from the second urn. What is the probability of winning the Mega Millions with a single ticket?

Two of a Kind Follow the outline presented in Problem 67 to determine the probability of being dealt exactly one pair.