4. Probability

In a survey, people are classified based on whether they can see the sunrise, the sunset, both, or neither. Which of the following best describes the joint relative frequency for the people who can only see the sunset?

The following represent the results of a survey in which individuals were asked to disclose what they perceive to be the ideal number of children.

b. What is the probability an individual is female and believes the ideal number of children is 2?

Using Probabilities for Significant Events

a. Find the probability of getting exactly 1 match.

In a standard deck of $52$ playing cards, what is the probability of not drawing a face card (Jack, Queen, or King) in a single random draw?

Lingo

In the gameshow Lingo, the team that correctly guesses a mystery word gets a chance to pull two Lingo balls from a bin. Balls in the bin are labeled with numbers that match the numbers still on the team's Lingo board. There are also three prize balls and three red "stopper" balls in the bin. If a stopper ball is drawn first, the team loses its second draw. To form a Lingo, the team needs five numbers in a row—vertically, horizontally, or diagonally. Consider the sample Lingo board below for a team that has just guessed a mystery word.

c. What is the probability that the team makes a Lingo on their first draw?

College Survey In a national survey conducted by the Centers for Disease Control to determine college students’ health-risk behaviors, college students were asked, “How often do you wear a seatbelt when driving a car?” The frequencies appear in the following table:

a. Construct a probability model for seatbelt use by a driver.

"Simulating Election Results

Suppose that polls indicate a candidate in a local school board election has the support of 52% of voters.

a. Explain how you could use the integers from 1 to 100 to simulate votes.

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In Exercises 9–20, use the data in the following table, which lists survey results from high school drivers at least 16 years of age (based on data from “Texting While Driving and Other Risky Motor Vehicle Behaviors Among U.S. High School Students,” by O’Malley, Shults, and Eaton, Pediatrics, Vol. 131, No. 6). Assume that subjects are randomly selected from those included in the table. Hint: Be very careful to read the question correctly.

Drinking and Driving If one of the high school drivers is randomly selected, find the probability of getting one who drove when drinking alcohol.

[NW] [DATA] TelevisionsIn the Sullivan Statistics Survey I, individuals were asked to disclose the number of televisions in their household. In the following probability distribution, the random variable X represents the number of televisions in households.

e. What is the probability that a randomly chosen household has three televisions?

Playing Five-Card Stud

In the game of five-card stud, each player is dealt one card face down and four cards face up. After two cards are dealt (one down, one up), players bet, and betting continues after each additional card is dealt. Suppose three cards have been dealt to each of five players at the table. You currently have three clubs and are trying to get a flush (all cards of the same suit). Of the cards dealt, two clubs are visible in other players' hands.

e. Should you continue playing the game?

Lottery. In Exercises 15–20, refer to the accompanying table, which describes probabilities for the California Daily 4 lottery. The player selects four digits with repetition allowed, and the random variable x is the number of digits that match those in the same order that they are drawn (for a “straight” bet).

Using Probabilities for Significant Events

a. Find the probability of getting exactly 2 matches.

Suppose the probability that a flight is on time is $P(ext\{on\; time\})\; =0.70$, the probability that it is less than $5$ minutes late is $P(ext\{less\; than\; \}5ext\{\; min\; late\})\; =0.15$, and the probability that it is more than $5$ minutes late is $P(ext\{more\; than\; \}5ext\{\; min\; late\})\; =0.15$. What is the probability that the flight will be no more than $5$ minutes late (to 2 decimals)?

Which of the following best describes the difference between $univariate$ data and $bivariate$ data?

In the context of probability and statistics, what does the error (accuracy of a poll) expressed as a $\pm$ percentage most commonly represent?