Question

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 $\$ 2$ . 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.

          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 $\$ 2$ . 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.

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Added by Ryan Z.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Joanna Quigley

08/17/2022

Step 1

For Wager 1, the expected value is calculated as follows: - The probability of winning is 1/2, and the gain is $1. So, the expected gain is (1/2)*$1 = $0.50. - The probability of losing is also 1/2, and the loss is $1. So, the expected loss is (1/2)*$1 = Show more…

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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 $\$ 2$ . 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.

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