Probability help!

[spardawg]

The problem is: In a carnival game, the theoretical probability of winning is 4/25. This game costs $3 to play. Winning players recieve a $15 prize. What is the expected value for this game?
I know the expected value is the average winnings and I have to multiply the amount you win to how you win or the number of times you win, but the problem doesn't really give me that information. Can you help me, please?

 

[galactus]

The probability of winning is 4/25. But, after you buy the ticket, if you win, you win $12 net. Because 15-3=12.

But, if you lose with probability 21/25, you are in the hole $3.

So, the expected value is \(\displaystyle \frac{4}{25}\cdot 12+\frac{21}{25}(-3)\)

 

[spardawg]

So I would consider the probability of winning the amount of times you win? (I think that's what I'm trying to say :? )

 

[galactus]

You would consider how many tickets are bought. The problem implies 1 ticket.

 

[spardawg]

ohh. okay. thank you soooo much!