Expected Value of Gambling Game: Solve It Now!

[eatinbyzombies3]

Here is the question: You are playing a gambling game (silly, yea I know). The first part of the game is to throw a die. If it comes up a 3, you move on. Otherwise, you lose. The second part of the game entails pulling a card out of a standard deck. If it is a heart, you win $100. Otherwise, you lose. What is the expected value of the game?

Here is what I know: you have a 1 out of 6 chance of rolling a 3 and a 13 out of 52 (i hope) chance of pulling a heart.

I don't know how to get the answer that is needed. Can anyone help me?

 

[MarkFL]

Re: help, I am confused

Are you supposed to find the expected profit? If so, what is the buy-in to the game?

edit: I have edited the topic title to reflect the nature of the problem.

 

[eatinbyzombies3]

MarkFL,
I don't know. that is the question word for word that I have on my paper from my Professor. That is what is confusing, it just says "What is the expected value of the game?"

 

[MarkFL]

Are you given an answer that you are expected to be able to compute?

 

[Jameson]

\(\displaystyle E[X]=\sum_{x} x \cdot P[X=x]\)
That seems complicated but it's not so bad. Assuming there is no buy-in to play the game and that the only payout occurs when you get a 3 and a heart, the above equation simplifies to:

\(\displaystyle E[X]=100 \cdot P[X= \text{3 and a heart}]\)

Now you just need to figure out that probability of getting a 3 and a heart and you'll be done. :)