Probability Lecture: Card Game with Augustina

Key Concepts

• Event N: Drawing an eight
• Event F: Drawing a face card (Jack, Queen, King)
• Mutually Exclusive Events: Two events that cannot occur simultaneously

Finding Probability of Events N and F

• Objective: Find the probability that a card drawn is both an eight and a face card.
• Card Count:
  • Eights: 4 cards (one of each suit)
  • Face Cards: 12 cards (Jack, Queen, King for each suit)
• Probability of N and F:
  • No card is both an eight and a face card.
  • Probability (N ∩ F) = 0

Determining if Events are Mutually Exclusive

• Definition: Events are mutually exclusive if they cannot both happen at the same time.
• Conclusion: Since no card can be both an eight and a face card, Events N and F are mutually exclusive.

Addition Rules for Probabilities

• Always True Rule:
  • P(N ∪ F) = P(N) + P(F) - P(N ∩ F)
• Mutually Exclusive Rule (applicable since the events are mutually exclusive):
  • P(N ∪ F) = P(N) + P(F)

Calculating Probability Augustina Wins

• Winning Condition: Drawing an eight or a face card.
• Using Addition Rule for Mutually Exclusive Events:
  • P(N ∪ F) = P(N) + P(F)
  • Probability of drawing an eight, P(N) = 4/52
  • Probability of drawing a face card, P(F) = 12/52

Calculation

• Formula: P(N ∪ F) = 4/52 + 12/52
• Result: P(N ∪ F) = 0.3077 (31% chance of winning)

Future Work

• Next Topic: Calculating the probability that Augustina loses the game.

These notes summarize the lecture on probability concerning the card game played by Augustina, focusing on mutually exclusive events and calculating probabilities with addition rules.