A game is played by flipping three coins. If all three coins land heads up you win $15. If two coins lands heads up you win $5. If one coin lands heads up you win $2. If no coins land heads up you win nothing. If you play $4 to play, what are your expected winnings?

Prob (HHH) = 1/8

expected value = (1/8)(15) = 1.875
prob(HHT or HTH or THH) 3/8
expected winnings = (3/8)(5) = 1 .875
prob(HTT or THT or TTH) = 3/8
expected winnings = (3/8)(2) = .75
prob( TTT) = 1/8
expected winning = 0

total expected winnings = 4.5
to play the game costs $4
expected winnings = $0.50

Bet you won't see that game in Vegas.

Thank you Reiny.

To determine the expected winnings, we need to calculate the probability of winning each possible amount and multiply it by the respective amount, and then sum up these values.

Let's calculate the probability of each outcome first:

1. Probability of all three coins landing heads up:
There is 1 way out of 8 possible outcomes where all three coins land heads up: HHH.
So, the probability is 1/8.

2. Probability of exactly two coins landing heads up:
There are 3 ways out of 8 possible outcomes where exactly two coins land heads up: HHT, HTH, and THH.
So, the probability is 3/8.

3. Probability of exactly one coin landing heads up:
There are 3 ways out of 8 possible outcomes where exactly one coin lands heads up: HTH, THH, and HHT.
So, the probability is 3/8.

4. Probability of no coins landing heads up:
There is 1 way out of 8 possible outcomes where no coins land heads up: TTT.
So, the probability is 1/8.

Now we can calculate the expected winnings:

Expected winnings = (Probability of all three coins landing heads up) * ($15) +
(Probability of exactly two coins landing heads up) * ($5) +
(Probability of exactly one coin landing heads up) * ($2) +
(Probability of no coins landing heads up) * ($0)

Expected winnings = (1/8) * ($15) + (3/8) * ($5) + (3/8) * ($2) + (1/8) * ($0)

Expected winnings = $1.875 + $1.875 + $0.75 + $0

Expected winnings = $4.50

Therefore, your expected winnings from playing the game are $4.50.