Section 5.4 Day 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) =

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) =

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

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

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)

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

● ● ● ● ● 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)

● ● ● ● 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) =

● ● ● ● 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) =

● ● ● ● ● 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) =

● ● ● ● 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) =

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) =

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.

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.

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.

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.

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.

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.

Diabetes No Diabetes Total Blue Not Blue Total

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.

Diabetes No Diabetes Total Blue .95x Not Blue Total x

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.

Diabetes No Diabetes Total Blue .95x .05y Not Blue Total x y

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.

Diabetes No Diabetes Total Blue .95x .05y Not Blue Total x= .04(total) y

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.

Diabetes No Diabetes Total Blue .95x .05y Not Blue Total x= .04(total) y 100

Diabetes No Diabetes Total Blue .95x .05y Not Blue Total 4 y 100

Diabetes No Diabetes Total Blue .95x .05y Not Blue Total 4 96 100

Diabetes No Diabetes Total Blue 3.8 .05y Not Blue Total 4 96 100

Diabetes No Diabetes Total Blue 3.8 4.8 Not Blue Total 4 96 100

Diabetes No Diabetes Total Blue 3.8 4.8 8.6 Not Blue 0.2 91.2 91.4 Total 4 96 100

Diabetes No Diabetes Total 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?

Diabetes No Diabetes Total 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?

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

Diabetes No Diabetes Total 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?

Diabetes No Diabetes Total 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?

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Page 335, P32

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Page 335, P32 =

Page 335, P32

Page 337, E47

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Page 337, E47

Page 337, E47

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Page 337, E47

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Page 334, P26

Page 334, P26

Page 334, P26

Page 334, P26

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

Page 334, P29

Page 334, P29

Page 334, P29

Page 334, P29

Questions?