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:

P(Win both games)=P(Win first game)×P(Win second game)P(\text{Win both games}) = P(\text{Win first game}) \times P(\text{Win second game})

Given:

  • P(Win first game)=0.35P(\text{Win first game}) = 0.35
  • P(Win second game)=0.16P(\text{Win second game}) = 0.16

Now, we perform the multiplication:

P(Win both games)=0.35×0.16=0.056P(\text{Win both games}) = 0.35 \times 0.16 = 0.056

Thus, the probability of winning both games is:

0.056 or 5.6%\boxed{0.056} \text{ or } 5.6\%

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Here are 5 related questions:

  1. What is the probability of winning at least one of the two games?
  2. What is the probability of winning only the first game?
  3. What is the probability of winning only the second game?
  4. How would the probability change if the two games were not independent?
  5. 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