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The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset Vaia Explanations$ Math

6th Edition · 837 pages

ISBN: 9781319113339

Chapter 5: Q. T5.9 (page 357)

Suppose that a student is randomly selected from a large high school. The probability
that the student is a senior is $0.22 .$ The probability that the student has a driver’s license
is $0.30$ . If the probability that the student is a senior or has a driver’s license is $0.36$ ,
what is the probability that the student is a senior and has a driver’s license?
$a . 0.060 b . 0.066 c . 0.080 d . 0.140 e . 0.160$

Short Answer

Expert verified

The correct option is:

$e . 0.160$

Step by step solution

01

Given information

We have to find is the probability that the student is a senior and has a driver’s license?

02

Explanation

His coach sends him to a summer clinic to work on his shot.
$0.160$ is the probability that the student is a senior and has a driver’s license.

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Most popular questions from this chapter

Mac or PC? A recent census at a major university revealed that $60 %$ of its students mainly used Macs. The rest mainly used PCs. At the time of the census, $67 %$ of the school’s students were undergraduates. The rest were graduate students. In the census, $23 %$ of respondents were graduate students and used a Mac as their main computer. Suppose we select a student at random from among those who were part of the census. Define events G: is a graduate student and M: primarily uses a Mac.

a. Find P(G ∪ M). Interpret this value in context.

b. Consider the event that the randomly selected student is an undergraduate student and

primarily uses a PC. Write this event in symbolic form and find its probability.

Who’s paying? Abigail, Bobby, Carlos, DeAnna, and Emily go to the bagel shop for lunch every Thursday. Each time, they randomly pick $2$ of the group to pay for lunch by drawing names from a hat.

a. Give a probability model for this chance process.

b. Find the probability that Carlos or DeAnna (or both) ends up paying for lunch.

Is this your card? A standard deck of playing cards (with jokers removed) consists of 52 cards in four suits—clubs, diamonds, hearts, and spades. Each suit has 13 cards, with denominations ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. The jacks, queens, and kings are referred to as “face cards.” Imagine that we shuffle the deck thoroughly and deal one card. The two-way table summarizes the sample space for this chance process based on whether or not the card is a face card and whether or not the card is a heart.

Type of card
	Face card	Non-Face card	Total
Heart	$3$	$10$	$13$
Non-Heart	$9$	$30$	$39$
Total	$12$	$40$	$52$

Are the events “heart” and “face card” independent? Justify your answer.

Random assignment Researchers recruited $20$ volunteers- $8$ men and $12$ women-to take part in an experiment. They randomly assigned the subjects into two groups of $10$ people each. To their surprise, $6$ of the $8$ men were randomly assigned to the same treatment. Should they be surprised? We want to design a simulation to estimate the probability that a proper random assignment would result in $6$ or more of the $8$ men ending up in the same group.

Get $20$ identical slips of paper. Write " $M$ " on $8$ of the slips and " $W$ " on the remaining $12$ slips. Put the slips into a hat and mix well. Draw $10$ of the slips without looking and place into one pile representing Group $1$ . Place the other $10$ slips in a pile representing Group $2$ . Record the largest number of men in either of the two groups from this simulated random assignment. Repeat this process many, many times. Find the percent of trials in which $6$ or more men ended up in the same group.

The partially complete table that follows shows the distribution of scores on the AP®

Statistics exam for a class of students.

Select a student from this class at random. If the student earned a score of 3 or higher

on the AP® Statistics exam, what is the probability that the student scored a 5?

a . 0.150 b . 0.214 c . 0.300 d . 0.428 e . 0.700

See all solutions

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