Questions: 12:24PM Mon Oct 14 myopenmath.com Score: 16.58/117 Answered: 18/117 Question 25 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 6. 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? Select an answer

12:24PM Mon Oct 14 myopenmath.com Score: 16.58/117 Answered: 18/117 Question 25 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 6. 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? Select an answer
Transcript text: 12:24PM Mon Oct 14 myopenmath.com Score: 16.58/117 Answered: 18/117 Question 25 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 $\$ 6$. 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. \$ $\square$ b) What is North's expected value for this game? Round your answer to the nearest cent. $\$$ $\square$ c) Who has the advantage in this game? Select an answer $\theta$ Submit Question
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Solution

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Solution Steps

Step 1: Calculate Kyd's Expected Value

To find Kyd's expected value, we consider the outcomes of the game:

  • If Kyd selects a face card (Jack, Queen, or King), he wins \$6. The probability of this event is \( P(\text{face card}) = \frac{12}{52} \).
  • If Kyd selects any other card, he loses \$3. The probability of this event is \( P(\text{non-face card}) = \frac{40}{52} \).

The expected value \( E(Kyd) \) can be calculated as follows:

\[ E(Kyd) = 6 \times P(\text{face card}) + (-3) \times P(\text{non-face card}) \] \[ E(Kyd) = 6 \times \frac{12}{52} + (-3) \times \frac{40}{52} = -0.92 \]

Step 2: Calculate North's Expected Value

North's expected value is the negative of Kyd's expected value since the game is zero-sum:

\[ E(North) = -E(Kyd) = -(-0.92) = 0.92 \]

Step 3: Determine Who Has the Advantage

To determine who has the advantage, we compare the expected values:

  • Kyd's expected value: \( E(Kyd) = -0.92 \)
  • North's expected value: \( E(North) = 0.92 \)

Since \( E(North) > E(Kyd) \), North has the advantage in this game.

Final Answer

Kyd's Expected Value: \(\boxed{-0.92}\)

North's Expected Value: \(\boxed{0.92}\)

Advantage: \(\boxed{\text{North}}\)

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