Conditional Probability

Question 1

Definition

Answer 1

P(A|B) = P(A intersection B)/P(B)

Question 2

P(S|A)

Answer 2

P(S|A) = 1

Question 3

True or False

P(B|A^c) = 1 - P(B|A)

Answer 3

False

P(B^c|A) = 1 - P(B|A)

Question 4

True or False

P(B1 union B2| A) = P(B1|A) + P(B2|A) - P(B1 inter B2| A)

Answer 4

True

Question 5

Write the conditional backwards for

P(An | A1 inter A2 inter… inter A(n-1))

Answer 5

P(An | A1 inter A2 inter… inter A(n-1))

*

P(A(n-1) | A1 inter A2 inter… inter A(n-2))

* … *

P(A1)

Question 6

Law of Total Probability

Answer 6

Let B1,B2,…,Bk form a partition of S.

P(A) = SUM over 1<= i <=k P(A|Bi)P(Bi)

Question 7

Bayes’ Theorem

Answer 7

P(A|B) = P(B|A) P(A)/P(B)

Question 8

When do we use Bayes’ Theorem?

Answer 8

We use it when finding the other conditional is easier.

Question 9

In the world of medical diagnosis P(Pos|Disease) is called…

Answer 9

sensititvity

Question 10

n the world of medical diagnosis P(Neg|Disease) is called…

Answer 10

Specificity

Question 11

n the world of medical diagnosis P(Disease) is called…

Answer 11

disease prevalence

Question 12

n the world of medical diagnosis P(Disease|Pos) is called…

Answer 12

Positive predicted value

Question 13

Notice: to find the positive predicted value of a test we need to have all three:

• P(Pos|D) sensitivity
• P(Neg|D) specificity
• P(D) disease prevalence