You roll a die. If an odd number comes up, you lose. If you get a 6, you win $54. If it is an even number other than 6, you get to roll again. If you get a 6 the second time, you win $18. If not, you lose.

Question

(a) Construct a probability model for the amount you win at this game. Explain briefly how you obtain the probabilities
associated with the different
amounts of winning.

Let X be the payoff.
E(X) = $54(1/6) + $18(1/2) + $0(1/2) +$0(1/2)
= $18

not sure if that's correct

Answer 1

Hmmm. I see it as

$54(1/6) + (1/2)($18(1/6)) = $12

Answer 2

are you even trying? #QUTISCOMINGFORYOU