https://file.aiquickdraw.com/mathbot/file/1727554485761ehi3v6ct.jpg

To solve this problem, let's break it down and calculate the expected values for both Kyd and North.

### a) Kyd's Expected Value:
1. **Number of Face Cards**: There are 12 face cards (Jack, Queen, King) in a standard 52-card deck (3 face cards in each of the 4 suits).
2. **Number of Other Cards**: There are 40 other cards (52 total cards - 12 face cards).
3. **Payouts**:
   - If Kyd selects a face card, North pays him $5.
   - If Kyd selects a non-face card, Kyd pays North $3.

We will now calculate the expected value for Kyd.

\[
\text{Expected value for Kyd} = \left(\frac{12}{52} \times 5\right) + \left(\frac{40}{52} \times -3\right)
\]

Let me compute that for you.The expected value for Kyd in this game is approximately **-1.15 dollars**.

### b) North's Expected Value:
Since North and Kyd are playing a zero-sum game (what one wins, the other loses), North's expected value will be the opposite of Kyd's.

\[
\text{Expected value for North} = - (\text{Expected value for Kyd}) = 1.15 \text{ dollars}
\]

### c) Who has the advantage?
Since Kyd has a negative expected value (-$1.15), North has the advantage in this game.

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Would you like any further details on the calculations, or do you have any questions?

Here are 5 related questions:
1. How would the expected values change if the payouts were adjusted?
2. What is the probability that Kyd wins money in a single draw?
3. How does the concept of expected value apply in other games of chance?
4. How would adding Jokers to the deck affect the game's balance?
5. Can this game be considered fair, and why?

**Tip**: Always consider both the probability of an event and the payout when calculating expected values in games of chance.

Kyd and North are playing a game. Kyd selects one card from a standard 52-card deck. If Kyd selects a face card (Jack, Queen, or King), North pays him $5. If Kyd selects any other type of card, he pays North $3. 
a) What is Kyd's expected value for this game? Round your answer to the nearest cent. 
b) What is North's expected value for this game? Round your answer to the nearest cent. 
c) Who has the advantage in this game?

Learn how to calculate the expected value for a game involving Kyd selecting a card from a 52-card deck. This problem involves concepts of probability and expected value, suitable for high school students in Grades 9-12.

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