Int2 section 4-5 1011

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Independent and Dependent Events

Independent and Dependent Events

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  • 1. SECTION 4-5 Independent and Dependent EventsFriday, December 17, 2010
  • 2. ESSENTIAL QUESTIONS How do you find probabilities of dependent events? How do you find the probability of independent events? Where you’ll see this: Government, health, sports, gamesFriday, December 17, 2010
  • 3. VOCABULARY 1. Independent: 2. Dependent:Friday, December 17, 2010
  • 4. VOCABULARY 1. Independent: When the result of the second event is not affected by the result of the first event 2. Dependent:Friday, December 17, 2010
  • 5. VOCABULARY 1. Independent: When the result of the second event is not affected by the result of the first event 2. Dependent: When the result of the second event is affected by the result of the first eventFriday, December 17, 2010
  • 6. EXAMPLE 1 Matt Mitarnowski draws a card at random from a standard deck of cards. He identifies the card then replaces it in the deck. Then he draws a second card. Find the probability that both cards will be black.Friday, December 17, 2010
  • 7. EXAMPLE 1 Matt Mitarnowski draws a card at random from a standard deck of cards. He identifies the card then replaces it in the deck. Then he draws a second card. Find the probability that both cards will be black. P (Black, then black)Friday, December 17, 2010
  • 8. EXAMPLE 1 Matt Mitarnowski draws a card at random from a standard deck of cards. He identifies the card then replaces it in the deck. Then he draws a second card. Find the probability that both cards will be black. P (Black, then black) = P (Black)iP (Black)Friday, December 17, 2010
  • 9. EXAMPLE 1 Matt Mitarnowski draws a card at random from a standard deck of cards. He identifies the card then replaces it in the deck. Then he draws a second card. Find the probability that both cards will be black. P (Black, then black) = P (Black)iP (Black) 26 26 = i 52 52Friday, December 17, 2010
  • 10. EXAMPLE 1 Matt Mitarnowski draws a card at random from a standard deck of cards. He identifies the card then replaces it in the deck. Then he draws a second card. Find the probability that both cards will be black. P (Black, then black) = P (Black)iP (Black) 26 26 676 = i = 52 52 2704Friday, December 17, 2010
  • 11. EXAMPLE 1 Matt Mitarnowski draws a card at random from a standard deck of cards. He identifies the card then replaces it in the deck. Then he draws a second card. Find the probability that both cards will be black. P (Black, then black) = P (Black)iP (Black) 26 26 676 1 = i = = 52 52 2704 4Friday, December 17, 2010
  • 12. EXAMPLE 1 Matt Mitarnowski draws a card at random from a standard deck of cards. He identifies the card then replaces it in the deck. Then he draws a second card. Find the probability that both cards will be black. P (Black, then black) = P (Black)iP (Black) 26 26 676 1 = i = = = 25% 52 52 2704 4Friday, December 17, 2010
  • 13. EXAMPLE 2 Fuzzy Jeff takes a deck of cards and draws a card at random. He identifies it and does not return it to the deck. He then draws a second card. What is the probability that both cards are black?Friday, December 17, 2010
  • 14. EXAMPLE 2 Fuzzy Jeff takes a deck of cards and draws a card at random. He identifies it and does not return it to the deck. He then draws a second card. What is the probability that both cards are black? P (Black, then black)Friday, December 17, 2010
  • 15. EXAMPLE 2 Fuzzy Jeff takes a deck of cards and draws a card at random. He identifies it and does not return it to the deck. He then draws a second card. What is the probability that both cards are black? P (Black, then black) = P (Black)iP (Black)Friday, December 17, 2010
  • 16. EXAMPLE 2 Fuzzy Jeff takes a deck of cards and draws a card at random. He identifies it and does not return it to the deck. He then draws a second card. What is the probability that both cards are black? P (Black, then black) = P (Black)iP (Black) 26 25 = i 52 51Friday, December 17, 2010
  • 17. EXAMPLE 2 Fuzzy Jeff takes a deck of cards and draws a card at random. He identifies it and does not return it to the deck. He then draws a second card. What is the probability that both cards are black? P (Black, then black) = P (Black)iP (Black) 26 25 650 = i = 52 51 2652Friday, December 17, 2010
  • 18. EXAMPLE 2 Fuzzy Jeff takes a deck of cards and draws a card at random. He identifies it and does not return it to the deck. He then draws a second card. What is the probability that both cards are black? P (Black, then black) = P (Black)iP (Black) 26 25 650 25 = i = = 52 51 2652 102Friday, December 17, 2010
  • 19. EXAMPLE 2 Fuzzy Jeff takes a deck of cards and draws a card at random. He identifies it and does not return it to the deck. He then draws a second card. What is the probability that both cards are black? P (Black, then black) = P (Black)iP (Black) 26 25 650 25 = i = = ≈ 24.5% 52 51 2652 102Friday, December 17, 2010
  • 20. PROBLEM SETFriday, December 17, 2010
  • 21. PROBLEM SET p. 170 #1-25 “Most people would rather be certain they’re miserable than risk being happy.” - Robert AnthonyFriday, December 17, 2010