2 Probability

Question 1

Define Sample Space

Answer 1

The set of all possible outcomes of a statistical experiment.

Question 2

Define Complement

Answer 2

The complement of an event A with respect to sample space S is the subset of all elements of S that are not in A

Question 3

Define the union, the interception , and what it means to be mutually exclusive

Answer 3

Question 4

Define Probability

Answer 4

Is a measure of a likelihood (chance) that a specific event will occur. The probability of an event lies in, the range of zero to one, where P(A)=1 if it is a sure thing and P(B)=0 if the event will never happen. Note that the sum of the probabilities of all events in the sample space for an experiment is always 1.

Question 5

What are the Additive Rules for Probability ?

Answer 5

1.) P(A U B) = P(A) + P(B) - P(A and B)

2.) P(A and B) = P(A) + P(B) - P(A U B)

3.) P(A’) = 1 - P(A) (compliment rule)

Question 6

Probability Laws

Answer 6

Question 7

The conditional probability of B, given A happens, denoted P(B|A) is:

Answer 7

P(B|A) = P(A and B)/(P(A), where P(A) > 0

Question 8

Addition Rule

Answer 8

**P(A U B) = P(A)+P(B)-P(A and B)

Question 9

Define the Multiplication Rule(Joint Probability Rule)

Answer 9

• The probability of the intersection of two events “and”

P(A and B)=P(A|B)P(B)= P(B|A)P(A)=P(B and A)

Question 10

What are independent events and give an example

Answer 10

Occurrence of one event does not affect the probability of the occurrence of the other event

• flipping coin, rolling die, finding a penny and drinking water

Question 11

What are dependent events and give an example

Answer 11

One event influences the probability of the other event.

• robbing a bank and going to jail, probability of a snow storm and probability that school will be closed

Question 12

How to show that two events are independent?

Answer 12

1.) P(A|B) = P(A)

2.) P(B|A) = P(A)

3.) P(A and B) = P(A)P(B)

Question 13

How to show that two events are mutually exclusive?

Answer 13

If P(A and B) = 0

Question 14

Law of Total Probability

Answer 14

Question 15

Define Baye’s Rule

Answer 15

Question 16

Bayes Rule Example 1

Answer 16

Question 17

Bayes Rule Example 2

Answer 17

Question 18

What is the difference between:
1.) Prevalence,
2.) Sensitivity,
3.). Specificity

Answer 18

Prevalence - probability of having the disease

Sensitivity - probability of a positive test for people with the disease. (True Positive)

Specificity - Probability of a negative test for people without the disease. (True negative)

Question 19

Bayes Rule Prevalence example

Answer 19