Int2 section 4-5 1011

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Independent and Dependent Events

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Int2 section 4-5 1011

  1. 1. SECTION 4-5 Independent and Dependent EventsFriday, December 17, 2010
  2. 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. 3. VOCABULARY 1. Independent: 2. Dependent:Friday, December 17, 2010
  4. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 20. PROBLEM SETFriday, December 17, 2010
  21. 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

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