# Expected value problem

#### eatinbyzombies3

##### New member
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

Staff member
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
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

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

#### Jameson

$$\displaystyle E[X]=\sum_{x} x \cdot P[X=x]$$
$$\displaystyle E[X]=100 \cdot P[X= \text{3 and a heart}]$$