Question

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. Round to the second decimal place.

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?

Answer 1

Answer:

a) -0.1536

b) 0.1536

c) North has the advantage in this game

Step-by-step explanation:

We can calculate the probability as:

$\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

P(Face card) =

$=\dfrac{12}{52} = 0.2308$

P(Non-face card) =

$=\dfrac{40}{52} = 0.7692$

" If Kyd selects a face card, North pays him $6. If Kyd selects any other type of card, he pays North $2."

a) Kyd's expected value for this game

We can write the probability distribution for Kyd as:

Event:   Face Card    Non-face Card

      x:             +6             -2

  P(x):          0.2308      0.7692

$E(x) = \displaystyle\sum x_iP(x_i)\\E(x) = +6(0.2308) + (-2)(0.7692)\\E(x) = -0.1536$

Expected value for Kyd is -0.1536

b)  North's expected value for this game

We can write the probability distribution for North as:

Event:   Face Card    Non-face Card

      x:             -6               +2

  P(x):          0.2308      0.7692

$E(x) = \displaystyle\sum x_iP(x_i)\\E(x) = -6(0.2308) + (2)(0.7692)\\E(x) = 0.1536$

Expected value for North is 0.1536

c) Thus, North has the advantage in this game as the expected value for North is greater than the expected value for Kyd.