Learning Materials
Features
Discover
Chapter 5: Q. 54 (page 329)
Union and intersection Suppose C and D are two events such that P(C), P(D), and
P(C ∪ D). Find P(C ∩ D).
The P is.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Recycling Do most teens recycle? To find out, an AP® Statistics class asked an SRS of students at their school whether they regularly recycle. In the sample, students said that they recycle. Is this convincing evidence that more than half of the students at the school would say they regularly recycle? The dotplot shows the results of taking SRSS of students from a population in which the true proportion who recycle is .
a. Explain why the sample result (out of said "Yes") does not give convincing evidence that more than half of the school's students recycle.
b. Suppose instead that students in the class's sample had said "Yes." Explain why this result would give convincing evidence that a majority of the school's students recycle.
Cell phonesThe Pew Research Center asked a random sample of adult cell-phone owners from the United States their age and which type of cell phone they own: iPhone, Android, or other (including non-smartphones). The two-way table summarizes the data.
Suppose we select one of the survey respondents at random. What’s the probability that:
a. The person is not age to and does not own an iPhone?
b. The person is age to or owns an iPhone?
Airport securityThe Transportation Security Administration (TSA) is responsible for airport safety. On some flights, TSA officers randomly select passengers for an extra security check prior to boarding. One such flight had passengers—in first class and in coach class. Some passengers were surprised when none of the passengers chosen for screening were seated in first class. We want to perform a simulation to estimate the probability that no first-class passengers would be chosen in a truly random selection.
a. Describe how you would use a table of random digits to carry out this simulation.
b. Perform one trial of the simulation using the random digits that follow. Copy the digits onto your paper and mark directly on or above them so that someone can follow what you did.
c. In of the trials of the simulation, none of the passengers chosen was seated in first class. Does this result provide convincing evidence that the TSA officers did not carry out a truly random selection? Explain your answer.
An unenlightened gambler
a. A gambler knows that red and black are equally likely to occur on each spin of a
roulette wheel. He observes that consecutive reds have occurred and bets heavily on
black at the next spin. Asked why, he explains that “black is due.” Explain to the
gambler what is wrong with this reasoning.
b. After hearing you explain why red and black are still equally likely after reds on the
roulette wheel, the gambler moves to a card game. He is dealt straight red cards from
a standard deck withred cards and black cards. He remembers what you said and
assumes that the next card dealt in the same hand is equally likely to be red or black.
Explain to the gambler what is wrong with this reasoning.
The most common bet in craps is the “pass line.” A pass line bettor wins immediately if either a or ancomes up on the first roll. This is called a natural. What is the probability that a natural does not occur?
a.
b.
c.
d.
e.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App