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?

a) -0.1536

b) 0.1536

c) North has the advantage in this game

Step-by-step explanation:

We can calculate the probability as:

P(Face card) =

P(Non-face card) =

" 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

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

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.

yes.. it's proven to be 36.