Question

1. The probability of college students in the US is given by P(A)= 0.06. The probability of smoking in the US is given by P(B)=0.24. From past studies it was determined that the probability of randomly selecting someone that is a college student and smokes is given by P(A∩B) =0.01. Create a 2-way probability table modeling all combinations of A, ~A, B, and ~B based on the information provided.

Answer 1

from given information
P(A n ~B) =P(A)-P(A n B) =0.06-0.01 =0.05

P(~ A n B) =P(B)-P(A n B) =0.24-0.01 =0.23

P(~ A n ~ B) =1-P(A u B) =1-(P(A)+P(B)-P(A n B)) =1-(0.06+0.24-0.01)=0.71

from above below is probability contingency table":

	A	~A	Total
B	0.01	0.23	0.24
~B	0.05	0.71	0.76
Total	0.06	0.94	1