Asurvey 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)?

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

Step-by-step 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.

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation:

x = -5

step-by-step explanation: