SOLUTION: A game involves selecting a card from a regular 52-card deck and tossing a coin. The coin is a fair coin and is equally likely to land on heads or tails. • If the card is a

Question 1206558: A game involves selecting a card from a regular 52-card deck and tossing a coin. The coin is a fair coin and is equally likely to land on heads or tails.
• 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, no matter what the coin shows.
Find the expected value for this game (expected net gain or loss). (Round your answer to two decimal places.)
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
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.

Answer by ikleyn(52810)   (Show Source): You can put this solution on YOUR website!
.
A game involves selecting a card from a regular 52-card deck and tossing a coin.
The coin is a fair coin and is equally likely to land on heads or tails.
• 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, no matter what the coin shows.
Find the expected value for this game (expected net gain or loss). (Round your answer to two decimal places.)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        @Theo produced many words, but made errors in his arithmetic calculastions; so, his answer is incorrect.
        He literally drown in a sea of words.

        I came to bring a correct solution.

In all, there are 52 cards in a standard deck; of them, 4*3 = 12 are face cards. P(face card and coin lands on Head) = = = . P(face card and coin lands on Tail) = = = . P(card is not face) = = = . The expected value of the game is E = + - = + - = = = -0.26923 (rounded). ANSWER. The expected value of the game is , or -0.26923 dollars per game, meaning loss of 0.26923 of a dollar per game, in average.

Solved.

RELATED QUESTIONS
A game involves selecting a card from a regular 52-card deck and tossing a coin. The coin (answered by Fombitz)
A game involves selecting a card from a regular 52-card deck and tossing a coin. The coin (answered by jim_thompson5910)
A game consists of tossing a fair die and then (blindly) selecting a card from a 52 card... (answered by Fombitz)
Which of the following is an example of dependent events? tossing a coin and... (answered by y6n3o9p4)
A card is drawn at random from a standard pack of playing cards. Then a fair coin is... (answered by greenestamps)
An experiment consists of tossing a coin, rolling a die and drawing a card from a... (answered by robertb)
What is the probability of flipping a coin and getting heads or drawing a face card from... (answered by Boreal)
A fair die is cast, a fair coin is tossed, and a card is drawn from a standard deck of 52 (answered by stanbon)
how many out comes are there when you toss a coin and pick a card from a deck of... (answered by Alan3354)