Answer:
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".
