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Section 5.4

Learn about conditional probability, the multiplication rule, and how to calculate conditional probabilities using examples.

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Section 5.4

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  1. Section 5.4 Day 2

  2. Conditional Probability For any two events A and B, where P(B) > 0, the probability of A given the condition B is: P(A B) =

  3. Conditional Probability For any two events A and B, where P(B) > 0, the probability of A given the condition B is: P(A B) =

  4. Multiplication Rule The Multiplication Rule is: P(A and B) =

  5. Multiplication Rule The Multiplication Rule is: P(A and B) = P(A)●P(B A) or

  6. Multiplication Rule The Multiplication Rule is: P(A and B) = P(A)●P(B A) or P(A and B) = P(B)●P(A B)

  7. ● ● ● ● ● Suppose Jack draws marbles at random, without replacement, from a bag containing three red and two blue marbles.

  8. ● ● ● ● ● Suppose Jack draws marbles at random, without replacement, from a bag containing three red and two blue marbles. Find these conditional probabilities. a) P(2nd draw is red 1st draw is red) b) P(2nd draw is red 1st draw is blue)

  9. ● ● ● ● Suppose Jack draws marbles at random, without replacement, from a bag containing three red and two blue marbles. Find these conditional probabilities. a) P(2nd draw is red 1st draw is red) =

  10. ● ● ● ● Suppose Jack draws marbles at random, without replacement, from a bag containing three red and two blue marbles. Find these conditional probabilities. a) P(2nd draw is red 1st draw is red) =

  11. ● ● ● ● ● Suppose Jack draws marbles at random, without replacement, from a bag containing three red and two blue marbles. Find these conditional probabilities. b) P(2nd draw is red 1st draw is blue) =

  12. ● ● ● ● Suppose Jack draws marbles at random, without replacement, from a bag containing three red and two blue marbles. Find these conditional probabilities. b) P(2nd draw is red 1st draw is blue) =

  13. Suppose Jack draws marbles at random, without replacement, from a bag containing three red and two blue marbles. Find these conditional probabilities. a) P(2nd draw is red 1st draw is red) = b) P(2nd draw is red 1st draw is blue) =

  14. Use the Multiplication Rule to find the probability that if you draw two cards from a deck without replacing the first before you draw the second, both cards will be hearts.

  15. Use the Multiplication Rule to find the probability that if you draw two cards from a deck without replacing the first before you draw the second, both cards will be hearts.

  16. Use the Multiplication Rule to find the probability that if you draw two cards from a deck and replacing the first before you draw the second, both cards will be hearts.

  17. Use the Multiplication Rule to find the probability that if you draw two cards from a deck and replacing the first before you draw the second, both cards will be hearts.

  18. Medi-Mart has just come out with a new diabetes test that registers blue (indicating diabetes) in 95% of users who have diabetes. However, the new test also registers blue in 5% of users who do not have diabetes. Suppose that, in reality, only 4% of people using this test have diabetes.

  19. Medi-Mart has just come out with a new diabetes test that registers blue (indicating diabetes) in 95% of users who have diabetes. However, the new test also registers blue in 5% of users who do not have diabetes. Suppose that, in reality, only 4% of people using this test have diabetes. Construct a table that reflects this situation.

  20. DiabetesNo DiabetesTotal Blue Not Blue Total

  21. Medi-Mart has just come out with a new diabetes test that registers blue (indicating diabetes) in 95% of users who have diabetes. However, the new test also registers blue in 5% of users who do not have diabetes. Suppose that, in reality, only 4% of people using this test have diabetes. Construct a table that reflects the situation.

  22. DiabetesNo DiabetesTotal Blue.95x Not Blue Totalx

  23. Medi-Mart has just come out with a new diabetes test that registers blue (indicating diabetes) in 95% of users who have diabetes. However, the new test also registers blue in 5% of users who do not have diabetes. Suppose that, in reality, only 4% of people using this test have diabetes. Construct a table that reflects the situation.

  24. DiabetesNo DiabetesTotal Blue.95x .05y Not Blue Totalx y

  25. Medi-Mart has just come out with a new diabetes test that registers blue (indicating diabetes) in 95% of users who have diabetes. However, the new test also registers blue in 5% of users who do not have diabetes. Suppose that, in reality, only 4% of people using this test have diabetes. Construct a table that reflects the situation.

  26. DiabetesNo DiabetesTotal Blue.95x .05y Not Blue Totalx= .04(total) y

  27. Medi-Mart has just come out with a new diabetes test that registers blue (indicating diabetes) in 95% of users who have diabetes. However, the new test also registers blue in 5% of users who do not have diabetes. Suppose that, in reality, only 4% of people using this test have diabetes. Construct a table that reflects the situation.

  28. DiabetesNo DiabetesTotal Blue.95x .05y Not Blue Totalx= .04(total) y 100

  29. DiabetesNo DiabetesTotal Blue.95x .05y Not Blue Total 4 y 100

  30. DiabetesNo DiabetesTotal Blue.95x .05y Not Blue Total 4 96 100

  31. DiabetesNo DiabetesTotal Blue3.8 .05y Not Blue Total 4 96 100

  32. DiabetesNo DiabetesTotal Blue3.8 4.8 Not Blue Total 4 96 100

  33. DiabetesNo DiabetesTotal Blue3.8 4.8 8.6 Not Blue 0.2 91.2 91.4 Total4 96100

  34. DiabetesNo DiabetesTotal Blue 3.8 4.8 8.6 Not Blue 0.2 91.2 91.4 Total 4 96 100 What is the probability that a randomly selected person who uses this test gets a blue result?

  35. DiabetesNo DiabetesTotal Blue 3.8 4.8 8.6 Not Blue 0.2 91.2 91.4 Total 4 96 100 What is the probability that a randomly selected person who uses this test gets a blue result?

  36. What is the probability that a randomly selected person who uses this test gets a blue result?

  37. DiabetesNo DiabetesTotal Blue 3.8 4.8 8.6 Not Blue 0.2 91.2 91.4 Total 4 96 100 What is the probability that a person has diabetes if the test registers blue?

  38. DiabetesNo DiabetesTotal Blue 3.8 4.8 8.6 Not Blue 0.2 91.2 91.4 Total 4 96 100 What is the probability that a person has diabetes if the test registers blue?

  39. Page 335, P32

  40. Page 335, P32

  41. Page 335, P32 2 10 20 24 6 30

  42. = Page 335, P32

  43. Page 335, P32

  44. Page 337, E47

  45. Page 337, E47

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  49. Page 337, E47

  50. Page 337, E47

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