I. Suppose that 55% of all adults regularly consume coffee, 45% regularly consum

Question

I. Suppose that 55% of all adults regularly consume coffee, 45% regularly consume carbonated soda, and 70% regularly consume at least one of these a. What is the probability that a randomly selected adult regularly con- b. What is the probability that a randomly selected adult doesn't regu- two types of drinks. sumes both coffee and soda? larly consume at least one of these two products? sumes coffee but does not regularly consume soda? c. What is the probability that a randomly selected adult regularly con- P(AUB)-P(A) +P(B)- PIAnB))

Explanation / Answer

Ans:

Let

A=adults regulary consumes coffee

B=adults regulary consumes soda

Given that

P(A)=0.55

P(B)=0.45

P(A or B)=0.70

a)P(A or B)=P(A)+P(B)-P(A and B)

0.7=0.55+0.45-P(A and B)

P(A and B)=0.55+0.45-0.7

P(A and B)=0.3

b)P(neither A nor B)=1-P(A or B)=1-0.7=0.3

c)P(A and not B)=P(A)-P(A and B)=0.55-0.3=0.25

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