CHAPTER 6 DAY 4

Warm – Up

The table below shows the distribution of races in a particular city in the United States.

Let A = person is Hispanic and Let B = person is White

Does the table represent the entire population? Find P(A) Find P(Bc) Find the probability the person is non-hispanic white.

Race Hispanic Not Hispanic

Asian 0.000 0.036

Black 0.003 0.121

White 0.060 0.691

Other 0.062 0.027

Homework #14-22

14. .540415. .667616. .0217. A. yes B. no, sum ≠ 1 C. yes18. A. .295 B. .348 C. .121119. A. yes B. .43 C. .96

D. .28 E. .7220. A. 1/38 B. 9/19 C. 6/1921. Row 122. First child = ¼ Both = 1/16

Neither = 9/16

The union of any collection of events is the event that at least one of the collection occurs. Notation for the union of A and B is A U B

The set A and B is also called the intersection of A and B, which is the set of all elements in both sets A and B. Notation for the intersection of sets A and B is A B

General Addition Rule for the Unions of Two Events

For any two events A and B,P(A or B) = P(A) + P(B) – P(A and B)P(A U B) = P(A) + P(B) – P(A B)

I

I

Venn Diagram to Show!

Example

Zack has applied to both Princeton and Stanford. He thinks that the probability that Princeton will admit him is 0.4, the probability that Stanford will admit him is 0.5, and the probability that both will admit him is 0.2.

Make a Venn Diagram marked with the given probabilities.

What is the probability that either Princeton or Stanford admits Zack? Use proper notation!

What is the probability that neither university admits Zack?

What is the probability that he gets into Stanford but not Princeton?

Independence is NOT Disjoint!

If two sets are independent their “picture” is intersecting.

Independence is NOT Disjoint!

If a picture of two sets is intersecting the two sets may or may not be independent!

If two sets are independent the following equation MUST be TRUE:

P A I B( ) =P A( )P B( )

Recall the warm-up…

The table below shows the distribution of races in a particular city in the United States.

Let A = person is Hispanic and Let B = person is White

Are the events A and B independent? Why or why not?

Race Hispanic Not Hispanic

Asian 0.000 0.036

Black 0.003 0.121

White 0.060 0.691

Other 0.062 0.027

Cautions…

Be sure to apply the correct addition rule. Use the general addition rule.

The multiplication rule applies only to independent events; you cannot use it if events are not independent.

Disjoint events are NEVER Independent