Question

A game consists of rolling a die. If you roll a 1 or 2 you win $5 . If you roll a 4,5, or 6 you pay $1.25

a) Determine the probability distribution for the winnings
b ) Determine the expected winnings
c) is this a fair game ?

Answer 1

a) Probability distribution

x P(x)

$5$ $\frac{1}{3}$

$-1.25$ $\frac{1}2{}$

$\frac{1}{6}$

b) $E(X)=5*\frac{1}{3}-1.25*\frac{1}{2}+0*\frac{1}{6}=\frac{25}{24}\approx\$1.04$

c) Since the expected gain does not equal 0, the game is not fair.