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 $4. 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?
Kyd
12/52 chance of a face card or 3/13
chance of any other card is 10/13
(3/13)(4)+(10/13)(-3)
North same except change the signs on the 4 and 3. Complete the math and see who gets the higher expected value.
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 $2. A) What is Kyd's expected value for this game? Round your answer to the nearest cent. $ bb) What is North's expected value for this game? Round your answer to the nearest cent. $ c) Who has the advantage in this game?
To calculate the expected value, we need to assign probabilities to the different outcomes of the game. Let's analyze the problem step by step.
Step 1: Determine the probability of Kyd selecting a face card. In a standard 52-card deck, there are 12 face cards (4 Jacks, 4 Queens, and 4 Kings) out of a total of 52 cards. Therefore, the probability of Kyd selecting a face card is 12/52, which simplifies to 3/13.
Step 2: Determine the probability of Kyd selecting a non-face card. The remaining cards in the deck that are not face cards consist of 40 cards (52 total cards - 12 face cards). Therefore, the probability of Kyd selecting a non-face card is 40/52, which simplifies to 10/13.
a) Kyd's expected value:
The expected value is calculated by multiplying each possible outcome by its respective probability and summing them up.
For selecting a face card:
Kyd wins $4 with a probability of 3/13, so the contribution of this outcome to the expected value is:
(3/13) * $4 = $12/13.
For selecting a non-face card:
Kyd loses $3 with a probability of 10/13, so the contribution of this outcome to the expected value is:
(10/13) * -$3 = -$30/13.
Summing up the contributions:
($12/13) + (-$30/13) = -$18/13.
Therefore, Kyd's expected value for this game is approximately -$1.38 when rounded to the nearest cent.
b) North's expected value:
Since Kyd's expected value is the negative of North's expected value, all we need to do is take the opposite sign. So, North's expected value is approximately $1.38 when rounded to the nearest cent.
c) In this game, Kyd has the advantage over North since his expected value is negative, meaning he can expect to lose money on average, while North's expected value is positive, meaning he can expect to win money on average.