Question

A game is suggested to you at a party. A person has the numbers 1 through 6 in a hat and asks that you pay them $1 to play. If you draw a 4 or a 5 you win $1. And if you draw the 6 you win $3.

Create a probability distribution for this game and determine its expected value.

The Expected Value is:

Answer 1

Solution:

Given data:

Let all the numbers from 1 to 6 are equally likely to come.

Let (X) be the winning (losing ) amount.

So, according to the problem you lose $1.Which yoou paid to play if 1,2 or 3 come that is, Probability of losing $1 = 3/6 = 1/2.

If you draw 4 or 5 you win $1 and since you alredy paid $1 that means no lose.If 4 or 5 come. So the probability that you lose = 2/6 =1/3.

And if you draw 6 you win $3 that is you gain $2 .So the probability that you gain is $2 =1/6.

X( in dollars)	-1	0	2
P(X)	1/2	1/3	1/6

E(X)= (-1*1/2)+(0*1/3)+(2*1/6)

= - 1/2 + 0 + 1/3

= -1/6.

The expected gain is negative .This is not a fair game.