Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Q 34. (page 373)

A deck of cards contains 52 cards, of which 4 are aces. You are offered the following

wager: Draw one card at random from the deck. You win \(10 if the card drawn is an ace.

Otherwise, you lose \)1. If you make this wager very many times, what will be the mean

amount you win?

a. About −,\(1because you will lose most of the time.

b. About\)9, because you win \(10but lose only \)1.

c. About -\(0.15; that is, on average, you lose about 15cents.

d. About \)0.77; that is, on average, you win about 77cents.

e. About $0, because the random draw gives you a fair bet.

Short Answer

Expert verified

c)-$0.15

Step by step solution

01

Step 1. Given information 

We have given values of win=$10 and loss=-$1

02

Step 2. To find the expected value to win.

P(win)=NumberoffavourableoutcomesNumberoftotaloutcomes=452=113P(loss)=NumberoffavourableoutcomesNumberoftotaloutcomes=4852=1213Now,μ=∑xP(x)=$10×113+(-$1)×1213=-$213≈-$0.15

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Get on the boat! A small ferry runs every half hour from one side of a large river to the other. The probability distribution for the random variable Y = money collected on a randomly selected ferry trip is shown here. From Exercise 7, μY=$19.35. Calculate and interpret the standard deviation of Y.

Using Benford's law According to Benford's law (Exercise 15, page 377), the probability that the first digit of the amount of a randomly chosen invoice is an 8 or a 9 is 0.097. Suppose you examine randomly selected invoices from a vendor until you find one whose amount begins with an 8 or a 9 .

a. How many invoices do you expect to examine before finding one that begins with an 8 or 9 ?

b. In fact, the first invoice you find with an amount that starts with an 8 or 9 is the 40 th invoice. Does this result provide convincing evidence that the invoice amounts are not genuine? Calculate an appropriate probability to support your answer.

10%condition To use a binomial distribution to approximate the count of successes in an SRS, why do we require that the sample size n be less than 10%of the population size N?

Taking the train According to New Jersey Transit, the 8:00A.M. weekday train from Princeton to New York City has a 90%chance of arriving on time on a randomly selected day. Suppose this claim is true. Choose 6 days at random. Let localid="1654594369074" Y=the number of days on which the train arrives on time.

.Life insurance The risk of insuring one person’s life is reduced if we insure many people. Suppose that we insure two 21-year-old males, and that their ages at death are independent. If X1andX2are the insurer’s income from the two insurance policies, the insurer’s average income W on the two policies is

W=X1+X22=0.5X1+0.5X2

Find the mean and standard deviation of W. (You see that the mean income is the same as for a single policy but the standard deviation is less.)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free