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

Short answer

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

Step-by-step solution

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 $\$2$.

Explanation 

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

The expected value for Wager$1$is higher, we prefer Wager $1$.