Probability dice roll questions

[mtingt]

Homework Statement

A player rolls a fair die and receives a number of dollars equal to the number of dots appearing on the face of the die. What is the least a player should expect to pay in order to play the game?

Homework Equations

I don't really understand the question?? can someone explain the questions or approach thanks

The Attempt at a Solution

 

[Mentallic]

I think it means what would the host of the game need to receive from each player in order to not win or lose any money in the long run. Players are going to be paid anywhere between 1 to 6 dollars each game they play, so I'm guessing the answer is the average?

I could be way off though.

 

[MarneMath]

I've actually seen this problem once or twice and in the end it is the average.

To see this, you just need to write down what the problem says:

$(1/6) + $(1/6) + $(1/6) + $ (1/6) + $(1/6) + $(1/6)

The $ represent the amount of money the person would get if a particular number is shown so for example, if 1 dot is shown the player gets 1 dollar, if 5 dots are shown the player gets 5 dollars, and so on and so forth.

 

[awkward]

In a probability class they would say that the roll of a die is a random variable. You are asked to find the expected value of the random variable.

The expected value does turn out to be the average in this case, but that is not true for all random variables.

 

[Ray Vickson]

In a probability class they would say that the roll of a die is a random variable. You are asked to find the expected value of the random variable.

The expected value does turn out to be the average in this case, but that is not true for all random variables.

This statement is highly misleading and likely wrong. For a single random variable, the average and the expected value are essentially the same, BY DEFINITION. If you have some other type of situation in mind, please tell us what it is. (Of course, in more advanced courses one can encounter random variables that do not have expected values, etc., but this would only be confusing to mention at all to a person taking a first course at an elementary level.)

A much mores serious objection is related to the issue of whether or not the expected value is really a relevant "fair price" in a one-shot situation (that is, in a situation in which you play the game just once). From the point of view of a casino, the expected value makes sense because the casino faces thousands of players and so is, in effect, playing many times. However, for an individual customer, the expected value may be a very poor way to decide whether the entry fee is too high or just right. All of this is connected to expected utility ideas.

RGV

 

[awkward]

Ray Vickson,

I take it you are disagreeing with my statement that the expected value is not, in general, the average? If so, allow me to point out that the previous posts in the thread seemed to be using "average" in the sense of the arithmetic mean of the values of the random variable. That is the sense I meant to refer to. But if you define "average" to mean "expected value", of course, that is a different proposition.

Sorry for any confusion, I should have been more explicit. "Average" is one of those ambiguous words.

 

[Ray Vickson]

Ray Vickson,

I take it you are disagreeing with my statement that the expected value is not, in general, the average? If so, allow me to point out that the previous posts in the thread seemed to be using "average" in the sense of the arithmetic mean of the values of the random variable. That is the sense I meant to refer to. But if you define "average" to mean "expected value", of course, that is a different proposition.

Sorry for any confusion, I should have been more explicit. "Average" is one of those ambiguous words.

I agree, and that is why I was careful to say "for a single random variable..."; however, the way I read you post, you were also talking about a single random variable, but maybe you really meant something different.

RGV