Question

A simple game goes as follows: you pay one dollar and roll a die. If the roll is either a 1 or 2, you get your dollar back. If it is greater than 3 you lose the dollar you paid. If it is a 3, you get your dollar back and an additional dollar. What is the expected value of the net amount of money you win/lose?

Answer 1

Answer:

-1/3

Step-by-step explanation:

Given that a simple game goes as follows: you pay one dollar and roll a die. If the roll is either a 1 or 2, you get your dollar back. If it is greater than 3 you lose the dollar you paid. If it is a 3, you get your dollar back and an additional dollar.

Your fee for the dollar would be 1 dollar always

If you roll 1 or 2, your gain is 0

If you roll 3, your gain is 1

If you roll 4 or 5 or 6you lose 1 dollar

Let X be the amount of gain.

X       0        1         -1

P       2/6     1/6      3/6  

E(x) = Sum of products of x with probabilities

= $\frac{1}{6} -\frac{3}{6} \\=\frac{-2}{6} \\=\frac{-1}{3}$

Note:  this is not a fair game to play since expected gain is negative.