Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

You buy a lottery ticket to a lottery that costs \(10 per ticket. There are only 100 tickets available to be sold in this lottery. In this lottery there are one \)500 prize, two \(100 prizes, and four \)25 prizes. Find your expected gain or loss.

Short Answer

Expert verified

The expected loss is-2.

Step by step solution

01

Given information

A lottery ticket costing $10.

Total tickets sold is 100.

The prizes are:1-$500,2-$100,4-$25.

02

Explanation

X
Px
XPx
490
1100
490×1100=4.9
90
2100
90×2100=4.9
15
4100
15×4100=0.6
-10
93100
-10×93100=-9.3
Total1
-2

Ex=X×Px

X is a random variable that defines the expected profit. There are few options when buying a ticket, the expected profit is 490because you won 500and you paid 10.

So, the difference is 490. Similarly, there are other probable profits are 90and15. If you do not win any prize you will lose 10.

We will have an expected loss of-2.

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.

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

Use the following information to answer the next five exercises: Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are 16business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested in the number of business majors in the sample.

Find the standard deviation.

The probability of a defective steel rod is 0.01. Steel rods are selected at random. Find the probability that the first defect occurs on the ninth steel rod. Use the TI-83+orTI-84 calculator to find the answer.

The chance of an IRS audit for a tax return with over $25,000 in income is about 2% per year. We are interested in the expected number of audits a person with that income has in a 20-year period. Assume each year is independent.

a. In words, define the random variable X.

b. List the values that X may take on.

c. Give the distribution of X. X ~ _____(_____,_____)

d. How many audits are expected in a 20-year period?

e. Find the probability that a person is not audited at all.

f. Find the probability that a person is audited more than twice

More than 96 percent of the very largest colleges and universities (more than 15,000 total enrollments) have some online offerings. Suppose you randomly pick 13 such institutions. We are interested in the number that offer distance learning courses.

a. In words, define the random variable X.

b. List the values that X may take on.

c. Give the distribution of X. X ~ _____(_____,_____)

d. On average, how many schools would you expect to offer such courses?

e. Find the probability that at most ten offer such courses.

f. Is it more likely that 12 or that 13 will offer such courses? Use numbers to justify your answer numerically and answer in a complete sentence.

Find the probability that a physics major will do post-graduate research for four years.

P(x=4)=_______

See all solutions

Recommended explanations on Math Textbooks

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