Question

Suppose that 51% of all adults regularly consume coffee, 63% regularly consume carbonated soda, and 72% regularly consume coffee OR carbonated soda.

Note: Your answer must have both side of probability definition . Hint P (?) =?

(a) (5 points) What is the probability that a randomly selected adult regularly consumes both coffee and soda? Draw Venn diagram and label (with probability) each portion of the diagram to answer this question.

(b) (2 points) What is the probability that a randomly selected adult regularly consume at most one of these two products?

(c) (2 points) What is the probability that a randomly selected adult consume none these two products?

Answer 1

Solution. Let_A_ All_adults regularly-consume coffee. 1 -- PCA) = slil.20:51 B! Alladults regularly consume carbonated مهمه KRE8.) 5 636 = 0.63 Hence A UB: regularly consume coffee or Carbonated Sada a. PCAUB) = 724 50.72 a) consider, Probability that a randomly I selected adult regularly consumes beth coffee . and sodd. lie PCADB) = p ) >> P CANB) = PCA)+PCB) - PCAUB) (ANB = Ost0.63 -0.72 LEPCANB) = 0.42 6 consider, Probability that a randomly selected adult regularly comsumes at most one of these two products jeA O B = Au Bor ACUBE or AC or Be KPADB) 02 jelper) = 1 CAUBU AFUBS)

(C) consider, Bobability that a sandomly selected adult consume none of these two products lie. P CAN B) » PCAUB) = 1-PCAUB) = -0.72 = 0.28 -P CAUB) = 0.28 (AUBIE

(C) consider, Bobability that a sandomly selected adult consume none of these two products lie. P CAN B) » PCAUB) = 1-PCAUB) = -0.72 = 0.28 -P CAUB) = 0.28 (AUBIE