A game is played by flipping three coins. If all three coins lands heads up you win $15. If two coin 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 you expected winnings?

Answer choice: a.)$1.00 b.) -$1.00 c.)-$0.50 d.)$0.50

P(3H) = 1/8

P(2H) = 3/8
P(1H) = 3/8
P(0h) = 1/8

expected winnings
3H ---> (1/8)15 = 1.875
2H ---> (3/8)5 = 1.875
1H ----> (3/8)2 = .75
0H -----> 0

total expected value = 3.5
but you paid $4.00
so you will lose $0.50

choice c) -.50

Thanks

To find the expected winnings, we need to compute the probability of each outcome and multiply it by the corresponding winnings.

There are 2 possible outcomes for each coin flip: heads (H) or tails (T).

1. All three coins land heads up:
The probability of getting heads on one coin flip is 1/2, so the probability of getting heads on all three coin flips is (1/2) * (1/2) * (1/2) = 1/8. The winnings for this outcome are $15.

2. Two coins land heads up:
The probability of getting heads on two coin flips is (1/2) * (1/2) * (1/2) for each possible combination of which two coins land heads up. There are three possible combinations: HTT, THT, TTH. So the total probability is 3 * (1/8) = 3/8. The winnings for this outcome are $5.

3. One coin lands heads up:
The probability of getting heads on one coin flip is 1/2, and there are three coins, so the total probability is 3 * (1/2) * (1/2) * (1/2) = 3/8. The winnings for this outcome are $2.

4. No coins land heads up:
The probability of getting tails on one coin flip is 1/2, so the probability of getting tails on all three coin flips is (1/2) * (1/2) * (1/2) = 1/8. The winnings for this outcome are $0.

Now we can calculate the expected winnings:

Expected winnings = (Probability of outcome 1 * Winnings for outcome 1) + (Probability of outcome 2 * Winnings for outcome 2) + (Probability of outcome 3 * Winnings for outcome 3) + (Probability of outcome 4 * Winnings for outcome 4)

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

Simplifying the equation, we get:

= ($15/8) + ($15/8) + ($6/8) + ($0/8)

= $36/8

= $4.50/1

Therefore, the expected winnings are $4.50. Since you paid $4 to play, your expected net winnings are $4.50 - $4 = $0.50.

Therefore, the correct answer is d) $0.50.