here is the question,

As part of a new poker promotion campaign, a casino is introducing a new game called flush that costs $0.25 to play; the game is based on a flush hand in poker in which a player holds all cards of the same suit. After paying $0.25 the player is dealt 5 cards from a deck of completely shuffled U.S playing cards. If all the cards are the same suit, then the player gets $100 back.
Q What is the probability of getting a flush?
Q Should the casino expect to win money ot lose money on this promotional game?

For the first part, I think p(flush)= 13/52x12/51x11/50x10/49x9/48
If a player gets a flush then the probability is multiplied by (100-0.25)=99.75

Can you tell me if this is correct. If it is, how do I answer the second question? I think people will be willing to pay at least a dollar to play the game (so they will play four times). Does that change anything?

Corrected

The probability of getting a flush in poker(not counting straight or royal flushes):

We choose 5 cards from the same suit of which there are 13 choices, C(13,5)

There are 4 suits, so we choose 1 of those. C(4,1)

Now, subtract the number of straight and royal flushes, which is 40.



The prob. Is then

Or about a .2% prob.

If you want to count the royal and straight flushes, just add the 40 back in.