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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 鈭�,\(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,渭=鈭�xP(x)=$10脳113+(-$1)脳1213=-$213鈮�-$0.15

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Most popular questions from this chapter

Each entry in a table of random digits like Table Dhas probability $$ of being a 0 , and the digits are independent of one another. Each line of Table D contains 40 random

digits. The mean and standard deviation of the number of 0 s in a randomly selected line will be approximately

a. mean =0.1, standard deviation =0.05.

b. mean =0.1, standard deviation =0.1.

c. mean =4, standard deviation =0.05.

d. mean =4, standard deviation =1.90.

e. mean =4, standard deviation =3.60.

Lie detectors A federal report finds that lie detector tests given to truthful persons have probability 0.2 of suggesting that the person is deceptive. 11 A company asks 12 job applicants about thefts from previous employers, using a lie detector to assess their truthfulness. Suppose that all 12 answer truthfully. Let Y= the number of people whom the lie detector indicates are being deceptive.

a. Find the probability that the lie detector indicates that at least 10 of the people are being honest.

b. Calculate and interpret 渭Y渭Y.

c. Calculate and interpret 蟽Y蟽Y.

If Jeff keeps playing until he wins a prize, what is the probability that he has to play the game exactly 5 times?

a. (0.25)5

b. (0.75)4

c. (0.75)5

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e.(51)(0.75)4(0.25)51(0.75)4(0.25)

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Toothpaste Ken is traveling for his business. He has a new 0.85-ounce tube of toothpaste that's supposed to last him the whole trip. The amount of toothpaste Ken squeezes out of the tube each time he brushes varies according to a Normal distribution with mean 0.13ounces and standard deviation 0.02ounces. If Ken brushes his teeth six times during the trip, what's the probability that he'll use all the toothpaste in the tube? Follow the four-step process.
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