a game consists of tossing a coin and rolling an ordinary di

a game consists of tossing a coin and rolling an ordinary die. If the player tosses a head and rolls and even number, the player wins $3. Otherwise the player pays $1.

a. What is the expected value of this game?

b. Is this a fair game?

Solution

P(head) = 1/2 = 0.5
P(even number) = 3/6 = 0.5

P(player tosses a head and rolls and even number)
= P(head)*P(even number)
= 0.5*0.5
= 0.25

a.
P(winning) = 0.25
expected value = 3*0.25 + (-1)*(1-0.25)
= 0

b.
Yes