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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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