3. Suppose that 58% of all adults regularly consume coffee, 44% regularly consum

Question

3. Suppose that 58% of all adults regularly consume coffee, 44% regularly consume carbonated soda, 74% regularly consume at least one of these two products a)Let A be that an adult consumes coffee, B is the event that an adult consumes carbonated soda. Find (i) P(A'), (i) P(B') b)What is the probability that a randomly selected adult consumes both coffee and soda. Writ e this event in terms of A, B (union, intersection, complement etc) c)What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products (in other words does not consume either), write this again in terms of events A,B with intersection, union or complement as needed

Explanation / Answer

P(A)=0.58

P(B)=0.44

P( A or B)=0.74

P(A and B)= P( A )+P( B)- P( A or B)=0.58+0.44-0.74=0.28

(a) P(A')=P(A or B)-P(A)=0.74-0.58=0.16

P(B')=P(A or B)-P(B)=0.74-0.44=0.30

(b) answer intersection

P(consuming both coffee and soda )=P(A and B)=P(A intersection B)=

P(A and B)=P( A )+P( B)- P( A or B)=0.58+0.44-0.74=0.28

(c) answer P((AUB)')

P(not consuming either)=P((AUB)')=1-P(AUB)=1-0.74=0.26

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