Question

To introduce a new beer, a company conducted a survey. It divided the U.S. into four regions: eastern, northern, southern, and western. The company estimates that 35% of the potential customers for the beer are in the eastern region, 30% are in the northern region, 20% are in the southern region, and 15% are in the western region. The survey indicates that 50% of the potential customers in the eastern region, 40% of the potential customers in the northern region, 36% of the potential customers in the southern region, and 42% of those in teh western region will buy the beer. If a potential customer chosen at random indicates that he or she will buy the beer, what is the probability that the customer is from the southern region?

Answer 1

Assmate Date Page Answer) het A. = Pernon A = Person is A = Person is Ay = Pernon in is from from from from the eartern region the northern region the Southern region the western region P(A) = 0.35 P(A) = 0.30 P(A₂) = 0.20 P(Ay) = 0.15 lot в Раллоn qi buу thе Балл We know P(BIA) = 0.50 P (BA) = 0.40 P(B/A) = 0.36 P(B/ Ay) = 0.42 We require P(A/B) PCE) = P(A,). P (BIA) + P (A.). P (6 (A)+F(A). POAT + P(Ay). Play We require = 0.35 (0.50) + 0.30(0.40) + 0.20 (0.36+0.15 (0.42) = 0.43 Now, we will Bayes theorem- P(A/B) = P(A) . P (BIA) 2 0.2060.36) T PCA, (B) = 0.167 2020-4-8 00:22 PE)