MHB Expected Value of Gambling Game: Solve It Now!

AI Thread Summary
The discussion focuses on calculating the expected value of a gambling game involving rolling a die and drawing a card from a deck. Participants note the probabilities: a 1 in 6 chance of rolling a 3 and a 1 in 4 chance of drawing a heart. The expected value can be computed using the formula E[X]=100 * P[X=3 and a heart], assuming no buy-in for the game. Clarification is sought on whether the expected profit or just the expected value is needed, but the main calculation hinges on determining the combined probability of both successful outcomes. Understanding these probabilities is essential to solving the problem correctly.
eatinbyzombies3
Messages
3
Reaction score
0
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?
 
Mathematics news on Phys.org
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.
 
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?"
 
Are you given an answer that you are expected to be able to compute?
 
$$E[X]=\sum_{x} x \cdot P[X=x]$$
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:

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

Now you just need to figure out that probability of getting a 3 and a heart and you'll be done. :)
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top