# Thread: Probability Probelms & Counting Techniques

1. ## Probability Probelms & Counting Techniques

you guys have been such a big help lol. i have... i think just one maybe two more question that i need help with.

You play a coin toss game with your friend. The game is that you toss three coins. If ALL heads or ALL tails come up, your friend pays you 4$. If any other combination appears, you pay your friend 1.50$

a) show (using expectation) that this game is unfair.

b) to whom is this game unfair?

2. Originally Posted by 16sammy
you guys have been such a big help lol. i have... i think just one maybe two more question that i need help with.

You play a coin toss game with your friend. The game is that you toss three coins. If ALL heads or ALL tails come up, your friend pays you 4$. If any other combination appears, you pay your friend 1.50$

a) show (using expectation) that this game is unfair.

b) to whom is this game unfair?
Pr(3 heads) + Pr(3 tails) = (1/2)^3 + (1/2)^3 = 1/4.

Let X be the random variable amount of money won by you in a game.

E(X) = (1/4)(4) + (3/4)(-1.5) = ......

If the game is fair, E(X) = 0.

If E(X) < 0, the game is unfair to you (why?)

If E(X) > 0, the game is unfair to your friend (why?).

3. The pmf is

xi : p(xi)
4 : .125
-1.5 : .125
-1.5 : .125
-1.5 : .125
-1.5 : .125
-1.5 : .125
-1.5 : .125
4 : .125

and so E(X) = x1p(x1)+...+x8p(x8) = -.125

4. well actually if the game is unfair it wont equal 0. the way u figure it out it will give u negative or positive number. if its negative its bad for u it its positive its good for u.

that i know. im just not good at getting the math of it.

5. Originally Posted by 16sammy
well actually if the game is unfair it wont equal 0. the way u figure it out it will give u negative or positive number. if its negative its bad for u it its positive its good for u.

that i know. im just not good at getting the math of it.
So what in my reply do you not understand?

6. sorry i misread one thing. but i cant just put e(x) <0... i have to have actual answers. so im assuming that if i punch that in my calc. it will give me answer lol...

idk its just a little confusing...

7. Originally Posted by 16sammy
sorry i misread one thing. but i cant just put e(x) <0... i have to have actual answers.
[snip]
That would probably be why I wrote:

E(X) = (1/4)(4) + (3/4)(-1.5) = ......

The ...... means that the final bit of arithmetic was left for you to do.

I really don't see why this question is still causing you so much trouble.

8. because i did that... and its not the right answer. i asked someone else and he was like... who ever told u that has no idea what hes talking about. he already did this nd got it right.

9. Originally Posted by 16sammy
because i did that... and its not the right answer. i asked someone else and he was like... who ever told u that has no idea what hes talking about. he already did this nd got it right.
Did what? Got what answer? And what answer did this friend of yours get? Perhaps in the future you should just get help from this friend of yours since clearly I have no idea what I'm talking about ......

10. i didn't say that did i? if i did im sorry i didnt mean it like that. i would get this friend to help but he wasnt online earlier. the answer isn't supposed to be 0.somethign cant remember. its a whole number. idk i havent gotten the answer yet he just told me how to do it. and it doesnt have a whole bunch of fractions in the equation.

11. Originally Posted by 16sammy
i didn't say that did i? if i did im sorry i didnt mean it like that. i would get this friend to help but he wasnt online earlier. the answer isn't supposed to be 0.somethign cant remember. its a whole number. idk i havent gotten the answer yet he just told me how to do it. and it doesnt have a whole bunch of fractions in the equation.

Originally Posted by mr fantastic
Pr(3 heads) + Pr(3 tails) = (1/2)^3 + (1/2)^3 = 1/4.

Let X be the random variable amount of money won by you in a game.

E(X) = (1/4)(4) + (3/4)(-1.5) = ......

If the game is fair, E(X) = 0.

If E(X) < 0, the game is unfair to you (why?)

If E(X) > 0, the game is unfair to your friend (why?).
Just where did I say E(X) = 0?

I said:

E(X) = (1/4)(4) + (3/4)(-1.5) = ......

Then I showed how the answer was to be interpreted:

If the game is fair, E(X) = 0.

If E(X) < 0, the game is unfair to you.

If E(X) > 0, the game is unfair to your friend.

NOTE: E(X) = (1/4)(4) + (3/4)(-1.5) = -1/8.

Those bunch of fractions in the equation (as you so quaintly call them) are actually a necessary part of getting the final answer.

12. Originally Posted by 16sammy
i didn't say that did i? if i did im sorry i didnt mean it like that. i would get this friend to help but he wasnt online earlier. the answer isn't supposed to be 0.somethign cant remember. its a whole number. idk i havent gotten the answer yet he just told me how to do it. and it doesnt have a whole bunch of fractions in the equation.
Since Mr Fantastic's reply is the correct answer to the question you have asked there are three possibilities: