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Expected value problem

eatinbyzombies3

New member
Jun 5, 2013
3
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 dont know how to get the answer that is needed. Can anyone help me?
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
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

New member
Jun 5, 2013
3
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

Administrator
Staff member
Feb 24, 2012
13,775
Are you given an answer that you are expected to be able to compute?
 

Jameson

Administrator
Staff member
Jan 26, 2012
4,040
\(\displaystyle E[X]=\sum_{x} x \cdot P[X=x]\)
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. :)