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Probability - Independent & Dependent Events
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Probability - Independent & Dependent Events

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  • 1. Using Probability
  • 2. Independent Events
    • Result of the first draw does not effect the outcome of the second draw.
    • Ex:
      • Event A - I draw a card from the bag. Then I put the card back in the bag.
      • Event B – I draw from the very same cards.
  • 3. Independent Events
    • If A & B are independent events, then I can find the probability of A and then B happening.
    • Multiply the events to find the probability of both events.
    • Formula
      • P(A & B) = P(A) x P(B)
  • 4. Independent Events
    • Example:
    • You have a bag of 15 scrabble tiles.
    • 3 of the tiles are the letter O.
    • What is the probability of getting an O ?
    • 3/15
    • 2 of the tiles are the letter U .
    • What is the probability of getting an U ?
    • 2/15
  • 5. Independent Events
    • What is the probability of getting O and then U ?
    • P(O) x P(U)
    • 3/15 x 2/15
    • 2/75
  • 6. Independent Events
    • Example:
    • You have a 52 cards.
    • 12 of the cards are the face cards .
    • What is the probability of getting a face card?
    • 12/52
    • 4 of the cards are the Aces.
    • What is the probability of getting an Ace?
    • 4/52
  • 7. Independent Events
    • What is the probability of getting a face card and then an Ace?
    • P(face card) x P(Ace)
    • 12/52 x 4/52
    • 3/169
  • 8. Dependent Events
    • When you don’t replace the first item before drawing the second item, the events are dependent.
    • Formula:
      • P(A&B) = P(A) x P(B after A)
  • 9. Dependent Events
    • Example:
    • You have a bag of 15 scrabble tiles.
    • 3 of the tiles are the letter O. What is the probability of getting an O on the first draw?
    • 3/15
    • 2 of the tiles are the letter U . What is the probability of getting an U if you didn’t replace the O ?
    • 2/14
  • 10. Dependent Events
    • What is the probability of getting O and then U if you don’t replace the O ?
    • P(O) x P(U after O)
    • 3/15 x 2/14
    • 1/35
  • 11. Dependent Events
    • Example:
    • You have a 52 cards.
    • 12 of the cards are the face cards . What is the probability of getting a face card?
    • 12/52
    • 4 of the cards are the Aces. What is the probability of getting an Ace if you don’t replace the face card?
    • 4/51
  • 12. Dependent Events
    • What is the probability of getting a face card and then an Ace without replacing the face card?
    • P(face card) x P(Ace after face)
    • 12/52 x 4/51
    • 4/221
  • 13. Review
    • Describe how to find the probability of two independent events.
    • Describe how to find the probability of two dependent events.

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