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# Probability - Independent & Dependent Events

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### Transcript

• 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.