Math Problem Statement
AP Statistics students designed a dice game that costs $1 to roll two fair dice once. If a player rolls doubles, they win $3 ($2 net gain). If they do not roll doubles, they lose their dollar (-$1 net gain). What is the expected net loss or gain for a player that rolls the dice one time?
Solution
Let's analyze the problem from the image:
Problem:
- A dice game costs $1 to play (a loss of $1 initially).
- Players roll two fair dice once:
- If the sum is a double (e.g., 2, 4, 6, etc.), they win $3 (resulting in a net gain of $2).
- If the sum is not a double, they lose their $1 entry fee (net gain of ).
- The task is to find the expected net loss or gain for a player.
Solution:
1
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Math Problem Analysis
Mathematical Concepts
Probability
Expected Value
Net Gain/Loss
Formulas
Expected Value = Σ (Probability × Outcome)
Theorems
Law of Total Expectation
Suitable Grade Level
Grades 10-12