Question

My friend and I are playing a gambling game in which we each roll a die. We then compare the numbers on the two dice to determine the outcome. If my roll is larger, I win $1 and my friend loses $1. If her roll is larger, I lose $1 and she wins $1. And if our two rolls are equal, we both don’t win or lose any money.

(a) Write your answers as simplified fractions: What is the chance I win $1? ___________ What is the chance I lose $1? ___________ What is the chance I don’t win or lose any money? ___________

(b) Based on your answers to (a), write down a box model for the amount I win or lose from one play of this game.

(c) The average of the tickets in the box from (b) is ___________ and the SD is ___________.

(d) Suppose my friend and I play the game 200 times. What is the chance I win $10 or more?

Answer 1

ANSWER::

We write sample size for roll of two dice. I won if 1st number is greater than 2nd number

a)

i) Chance I win $1 = 15/36

= 0.42

Ii) chance I lose $1 = 15/36

= 0.42

Chance I dont win or lose any money = 6/36

= 0.16

b)

Let X denote amount win

X = $1 with p=15/36

-$1 with p=15/36

0 with p = 6/36

c)

Average = 1(15/36) -1(15/36) + 0(6/36)

Average =0

E(X^2) = 1(15/36)+1(15/36)+0(6/36)

= 30/36

Variance = E(X^2) - [E(X)]^2

= 30/36

= 0.83

Standard deviation = sqrt(0.83)

= 0.91

d)

Let Y denote amount won from playing 200 games, Y = 200X. E(Y) =200E(X) =0,

Standard deviation Y = 200(sdX) = 182

P(Y>=10) = P(Z>=10/182)

= P(Z>= 0.05)

= 0.4801

NOTE:: I HOPE YOUR HAPPY WITH MY ANSWER....***PLEASE SUPPORT ME WITH YOUR RATING...

***PLEASE GIVE ME "LIKE"...ITS VERY IMPORTANT FOR ME NOW....PLEASE SUPPORT ME ....THANK YOU