Question 1206558
it has been pointed out that my solution is wrong.
i went back to see where i went wrong.
i think i found it.
the problem was not in the procedure.
it was in the arithmetic.
thanks to the other tutors who set me straight.
my apologies to the student that i provided an incorrect solution to.


here is the corrected solution.


if the card is a face card and the coin lands on heads, you win 9.
if the card is a face card and the coin lands on tails, you win 2.
if the card is not a face card, you lose 2.


there are 12 face cards in the deck.
4 jacks
4 queens
4 kinds


probability of getting a face card is 12/52.
probability of a coin landing on heads is 1/2.
probability of a coin landing on tails is 1/2.


probability of getting a face card and a coin landing on heads is 12/52 * 1/2 = 12/104 = 3/26.


probability of getting a face card and a coin landing on tails is 12/52 * 1/2 = 12/104 = 3/26.


probability of not landing on a face card is 40/52 = 20/26.


your expected value if you get a face card and flip heads is 9.
your expected value if you get a face card and flip tails is 2.
your expected value if you don't get a face card is -2.


your overall expected value is 3/26 * 9 + 3/26 * 2 - 20/26 * 2 = (27 + 6 - 40) / 26 = -7 / 26 = -.2692307692.


round to the nearest penny to get -.27.