Question

in a game, you toss a fair coin and a fair six sided die. if you toss a heads on the coin and roll either a 3 or a 6 on the die, you win $30. otherwise, you lose $6. what is the expected profit of one round of this game

Answer 1

P(Head) = 1/2

P(either 3 or 6) = p(roll 3) + P(Roll 6) = 1/6 + 1/6 = 2/6

P(Head) and P(Roll either 3 or 6) = 1/2 * 2/6 = 1/6

E(X) = Expected win - Expected loss

= 1/6 * 30 - ( 1 - 1/6) * 6

= 0