Question

KEY

Region 1 = NW Population 1 = Under 50,000

Region 2 = SW Population 2 = 50,000 - 100,000

Region 3 = NE Population 3 = Over 100,000

Region 4 = SE

Count of Population

	Region				Total
population	1	2	3	4
1	34	38	34	38	144
2	36	55	27	33	151
3	35	37	35	48	155
Total :	105	130	96	119	450

Big Burger is a fast food restaurant that has 450 locations all over the U.S. Use the excel output above to answer the following question.

Let event

A = Selected restaurant is not in the northeast            

B = Selected restaurant is in a city with a population size between 50,000 and 100,000      

Events A and B are __

Choose True (T) or False (F) for the following

1) dependent because P(A and B)≠0

2) independent because P(B|A)≠P(A)

3) dependent because P(A|B)≠P(B)

4) independent because P(A and B)≠P(B|A)*P(A)

5) dependent because P(A and B)=P(A)+P(B)

6) independent because P(A and B)=P(A)*P(B)

7) dependent because P(B|A)=P(A)

8) independent because P(A|B)=P(B)

9) dependent because P(A and B)=P(B|A)*P(A)

10) independent because P(A and B)≠P(A)+P(B)

11) dependent because P(A and B)≠P(A)*P(B)

12) independent because P(A and B)=0

Answer 1

P(A) =P(not in northeqast)=1-P(in northeast) =1-(region 3)=1-96/450=0.7867

P(B)=P(Population 2)=151/450=0.3356

P(A n B)=(36+55+33)/450=0.2756

P(B|A)=(36+55+33)/(450-96)=0.3503

P(A|B) =(36+55+33)/151=0.8212

1) dependent because P(A and B)≠0 --false

2)  independent because P(B|A)≠P(A) -- --false

3)  dependent because P(A|B)≠P(B) --false

4)  independent because P(A and B)≠P(B|A)*P(A) --false

5)  dependent because P(A and B)=P(A)+P(B) --false

6)  independent because P(A and B)=P(A)*P(B) --false

7) dependent because P(B|A)=P(A) -- false

8)  independent because P(A|B)=P(B) --false

9) dependent because P(A and B)=P(B|A)*P(A) --false

10)  independent because P(A and B)≠P(A)+P(B) --false

11)  dependent because P(A and B)≠P(A)*P(B) -- True

12)  independent because P(A and B)=0 --false