in a game, two regular dice are rolled.?

Question

if the sum is 8, the player recieves $8. if the sum is 10 the player recieves $ 10. otherwise there is no payoff. what is the expected payoff?

Answer 1

The "expected value" is the sum of all the outcome probabilities times the value from each outcome.

When rolling two dice, there are 36 possible outcomes which sum to 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12, with *differing probabilities* (e.g., there are many ways to roll two dice and get a sum of 7, but there is only one way to get a sum of 2). The expected value, then, is:

EV = Pr(total 2)*(value for rolling a total of 2) + Pr(total 3)*(value for rolling a total of 3) + Pr(total 4)*(value for rolling a total of 4) + ... + Pr(total 12)*(value for rolling a total of 12)

Since the value of rolling anything other than an 8 or 10 is 0, the other terms drop out of the equation. The EV is:

EV = Pr(total 8)*(value for rolling a total of 8) + Pr(total 10)*(value for rolling a total of 10)

So you just need to figure out the probability of getting a total of 8 or getting a total of 10 when rolling two dice and plug those into your equation.

edit: I did not get 2.22 as my answer.

Answer 2

What? The expected payoff is either $8 or $10 - there is no other payoff according to your definition.

Answer 3

you can do this

how many sides are there on each die?

so, if each die is differently colored, how many combinations of different sides of both dice are possible when you throw them both at the same time? [this is the number of posible throws of two honest regular dice]

***
how many of all the possible throws for the two dice together total to exactly eight pips showing?

how many of them total exactly ten pips?

***
so if you then throw exactly as many times as there are unique throws [part 1 above] and get each possible combination out of all the possible outcomes exactly once, how much money would you receive in all?

the expected payoff for one random throw is then this total amount divided by the number of possible unique throws that you calculated earlier.


your teacher will NOT give you credit for an answer without you being able to show your work, which I just laid out for you.


if you do not get 2.22 as your answer, please re-do the steps.


:-)

Answer 4

70/36, or ~1.95 dollars. the total number of possibilites is 36 for 2 die, and the total amount of money that you can receive for all those possibilites combined is 70 dollars. so on average, you will have a $1.95 payoff everytime you roll the die.

Answer 5

Why don't you ask wgos1955? You seem to ask the same questions. Hmmm.... wonder why?