mintsharpie

Can someone please look over the small chart I made that describes the probability game I made up and tell me if it's correct? In my game, the player picks three cards from a deck, placing each one to the side as they are chosen. If all three cards are the same colour, they win a certain amount of money. If the cards are any other combinatrion of red and black, they win nothing. P(x) is probability, and ? XP(x) is the expected winnings on average. Does this make sense?

Please help!

mathman

What is the meaning of X? You give it a value of 7. What is that?
What is x? You have defined it to mean 3 red cards, 3 black cards, or either event?

mintsharpie

X is the amount of money the player wins if they get three red or three black cards.

mathman

Your calculation of expected return on a bet is correct, although to be fair you need to subtract the cost of the bet.

skipjack

The probability that the second and third cards match the first is (25/51)(24/50), i.e., 4/17, so the expected return is 28/17. You don't need a chart for that and don't need to calculate anything to nine decimal places.