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Chapter 6: Q.30 (page 356)

The deck of 52cards contains 13hearts. Here is another wager: Draw one card at random from the deck. If the card drawn is a heart, you win 2. Otherwise, you lose 1. Compare this wager (call it Wager 2) with that of the previous exercise (call it Wager 1). Which one should you prefer?

(a) Wager 1, because it has a higher expected value.

(b) Wager 2, because it has a higher expected value.

(c) Wager 1, because it has a higher probability of winning.

(d) Wager 2, because it has a higher probability of winning. (e) Both wagers are equally favorable

Short Answer

Expert verified

The correct option is A (Wager 1, because it has a higher expected value).

Step by step solution

01

Given Information 

The deck of 52 cards contains 13 hearts. Here is another wager: Draw one card at random from the deck. If the card drawn is a heart, you win $2.

02

Explanation 

The expected value is the sum of the product of each possibility with its probability:

The expected value for Wager1is higher, we prefer Wager 1.

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Most popular questions from this chapter

A deck of cards contains 52cards, of which 4are aces. You are offered the following wager: Draw one card at random from the deck. You win \(10if the card drawn is an ace. Otherwise, you lose \)1. If you make this wager very many times, what will be the mean amount you win?

(a) About 鈭�\(1, because you will lose most of the time.

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

(c) About 鈭�\(0.15; that is, on average you lose about 15cents. (d) About \)0.77; that is, on average you win about 77cents.

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

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