Math Problem Statement
You play two unrelated games one after the other, there is a 35% chance of winning the first game and there is a 16% chance of winning the second game. What is the probability that you win both games?
Solution
To calculate the probability of winning both games, given that the events are independent, we multiply the individual probabilities:
Given:
Now, we perform the multiplication:
Thus, the probability of winning both games is:
Would you like to see further details or have any questions?
Here are 5 related questions:
- What is the probability of winning at least one of the two games?
- What is the probability of winning only the first game?
- What is the probability of winning only the second game?
- How would the probability change if the two games were not independent?
- What is the probability of losing both games?
Tip: When working with independent events, always multiply the individual probabilities for "AND" scenarios.
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Math Problem Analysis
Mathematical Concepts
Probability
Independent Events
Formulas
P(Win both games) = P(Win first game) × P(Win second game)
Theorems
Multiplication Rule for Independent Events
Suitable Grade Level
Grades 10-12
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