Finding P(x)

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fruit33

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Question: The game costs $2 to play and involves a participant randomly choosing two cards from a set consisting of only four queens and kings. If two queens or two kings are selected, the participant is paid $3. If a king and a queen of the same suit are selected, the participant is paid $5. If a king and a queen of different suits are selected, the participant loses the game.

I know that my discrete random variable X numbers are 0, 3 and 5.
How can I now find P(x)?
 
P(x=5) = P(K and Q of same suit)

How many such combinations are there?

Then do similarly for x=3; and for x=0, just subtract from 1.
 
First, "four queens and kings" is not an adequate description of the deck. Do you mean two of each? Something else?

Second, you have said nothing of the suits, except that we care about it when determining a winner. Do you mean King and Queen of two different suits? Or could they be from all four?

This is a VERY SMALL problem. Why not just write out the entire distribution?

Why are the outcomes 0, 3, and 5? Didn't you pay $2 to get into the game?
 
I like this game as the only outcomes, according to you, is that you win either $0, $3 or $5. So you can't lose! Please try again computing what the values for X can be, where X is the amount you can win (or lose).
 
tkhunny said:
First, "four queens and kings" is not an adequate description of the deck. Do you mean two of each? Something else?

Second, you have said nothing of the suits, except that we care about it when determining a winner. Do you mean King and Queen of two different suits? Or could they be from all four?
Click to expand...
You're right that the wording of the problem could be clearer, and I'm hoping to hear more about it. But I'm guessing it means "the four queens and the four kings from a standard deck of cards", so it would be 8 cards, 2 of each suit. I make that guess because it's the only interpretation I see in which information is not missing.

tkhunny said:
Why are the outcomes 0, 3, and 5? Didn't you pay $2 to get into the game?
Click to expand...
That's a good point; but in addition, we aren't told what X is, so it's possible the OP plans to make the adjustment for the cost later ...

@fruit33, would you like to quote the entire problem exactly, and define your terms, in addition to showing your work?
 
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