Question

A survey by Gallup asked a random sample of American adults about their soda consumption. Let's call X the number of glasses of soda consumed on a typical day. Gallup found the following probability X:X 0 1 2 3 4+Probability 0.52 0.28 0.09 0.04 0.07Consider the eventsA = {number of glasses of soda is 1 or greater}B = {number of glasses of soda is 2 or less A.}a) What outcomes make up the event A? What is P(A)?b) What outcomes make up the event B? What is P(B)?c) What outcomes make up the event "A or B"? What is P(A or B)? Why is this probability not equal to P(A) + P(B)?

Answer 1

a) Outcomes making up event A are (1,2,3,4+)

P(A) = 0.48

b) Outcomes making up event B are (0,1,2)

P(B) = 0.89

c) Outcomes making up event C are (0,1,2,3,4+)

P(A or B) = 1

Explanation:

a) P(A) = P(X = 1)+P(X = 2)+P(X = 3)+P(X = 4+)

= 0.28+0.09+0.04+0.07= 0.48

b) P(B) = P(X = 0)+P(X = 1)+P(X = 2)

= 0.52+0.28+0.09 = 0.89

c) A and B are non-mutually exclusive, they can both occur at the same time.

Thus, the probability that A or B will occur is given by:

P(A or B) = P(A) + P(B) - P(A∩B)

But P(A∩B)= P(X=1) + P(X=2)= 0.28+0.09=0.37

Hence, P(A or B) = 0.48+0.89-0.37 = 1

P(A or B) in not equal to P(A) + P(B) because events A and B are not mutually exclusive.