Three fair coins are tossed. If all land "heads," the player wins $10, and if exactly two land heads, the player wins $5. If it costs $4 to play, what is the player's expected outcome after four games?

After four games, a player can lose up to $ 16 to win up to $ 26. These are the probabilities for every game:

1/8 or 12.5% of landing three "heads"

3/8 or 37.5% of landing two "heads"

4/8 or 50% of landing no or only one "head".

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

If three coins land "heads" the player wins $ 10

If two coins land "heads" the player wins $ 5

Cost of playing = $ 4

2. What is the player's expected outcome after four games?

Probability of two coins out of three lands "heads" = 3/8

Probability of three coins out of three lands "heads" = 1/8

Now, let's calculate the player's expected outcome, as follows:

Four games:

Cost = 4 * 4 = $ 16

Worst-case scenario: No wins

Best-case scenario: 4 out of 4 of $ 10 win

Worst-case scenario profit or loss = 0 - 16 = Loss of $ 16

Best-case scenario profit or loss = 40 - 16 = Profit of $ 24

After four games, a player can lose up to $ 16 to win up to $ 26. These are the probabilities for every game:

1/8 or 12.5% of landing three "heads"

3/8 or 37.5% of landing two "heads"

4/8 or 50% of landing no or only one "head".