Ask Question
4 July, 19:14

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?

+2
Answers (1)
  1. 4 July, 20:54
    0
    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".
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “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 ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers