Complementary Probability

Key Concepts

• Complementary Events: Winning and losing are complementary events. If one happens, the other cannot.
  • In mathematical terms, the complement of winning is losing, and vice versa.
  • These events are mutually exclusive.

Probability Calculations

• Sample Space: The total probability of complementary events adds up to 1 (or 100%).
  • Formula: [ P(Win) + P(Lose) = 1 ]

Calculating Probability of Losing

• Given:
  • Probability Augustine wins: 0.3076923
• To find the probability of losing, use the complement rule:
  • [ P(Lose) = 1 - P(Win) ]
  • Calculation:
    • [ P(Lose) = 1 - 0.3076923 = 0.6923077 ]

Advantages of Using Complementary Probability

• Easier than directly calculating the probability of losing due to multiple possibilities.
• Direct calculation of losing involves considering all the other cards besides winning ones (e.g., drawing an eight or a face card for wins).
• Utilizing known probabilities simplifies the process.

Conclusion

• Understanding and using complementary probabilities can simplify calculations especially when one probability is easier to determine directly.