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. Diabetes No Diabetes Total
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. Diabetes No Diabetes Total
Blue x
Not Blue
Total x

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. Diabetes No Diabetes Total
Blue x .05y
Not Blue
Total x 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. Diabetes No Diabetes Total
Blue x .05y
Not Blue
Total x= .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. Diabetes No Diabetes Total
Blue x .05y
Not Blue
Total x= .04(total) y

29. Diabetes No Diabetes Total
Blue x .05y
Not Blue
Total y

30. Diabetes No Diabetes Total
Blue x .05y
Not Blue
Total

31. Diabetes No Diabetes Total
Blue y
Not Blue
Total

32. Diabetes No Diabetes Total
Blue
Not Blue
Total

33. Diabetes No Diabetes Total
Blue
Not Blue
Total

34. Diabetes No Diabetes Total
Blue
Not Blue
Total
What is the probability that a randomly selected person who uses this test gets a blue result?

35. Diabetes No Diabetes Total
Blue
Not Blue
Total
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. Diabetes No Diabetes Total
Blue
Not Blue
Total
What is the probability that a person has diabetes if the test registers blue?

38. Diabetes No Diabetes Total
Blue
Not Blue
Total
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

46. Page 337, E47

47. Page 337, E47

48. Page 337, E47

49. Page 337, E47

50. Page 337, E47

51. Page 334, P26

52. Page 334, P26

53. Page 334, P26

54. Page 334, P26

55. Order makes a difference!
Page 334, P26
Order makes a difference!

56. Page 334, P29

57. Page 334, P29

58. Page 334, P29

59. Page 334, P29

60. Questions?