Pick a Card.

Question

Mike and dave play the following card game. Mike picks a card from the deck
If he selects a heart Dave gives him $5, if not, he gives Dave $2.

Determine Mikes's expectation.

Determine Daves' expectation

Can you help me with this? i have tried to do it and i came up with (Mike's = -$1.58 and dave's = - $4.79) but I don't think the game is "fair" so I don't think the expected value is 0. I am really confused!

Answer 1

Prob(heart) = 1/4
prob(not a heart) = 3/4

Mike's expectation:
he will receive $5 if he picks a heart
expectation = 5(1/4) = $1.25
Dave's expectation:
he will receive $2 if Mike does not pick heart
expectation = $2(3/4) = $1.50

The game is clearly in Dave's favour.
If you wanted to know what Dave should receive to make it a "fair" game, let the amount Dave should receive be $x
x(3/4) = 5(1/4)
x = $1.67

(how ever did you get -$1.58 and -$4.79 ???????)