Two of the largest fast-food chains in the U.S. are McDonalds, Subway, and China

Question

Two of the largest fast-food chains in the U.S. are McDonalds, Subway, and China Great Wall. It is found that China Great Wall has outlets in 4% of foodcourts that have a MacDonald's, 10% of foodcourts have both a Subway and a China Great Wall. For a randomly choose food court, let M: It has a McDonalds franchise B: It has a Subway franchise C: It has a China Great Wall franchise (a) Indicate each correct answer (there may be more than one): (A) P (M|C) = 0.04 (B) P (C|M) = 0.04 (C) P (C Union M) = 0.04 (D) P (B|C) = 0.10 (E) P (C|B) = 0.10 (F) P (C Union B) = 0.10 (b) Use the given information to compute the percentage of food courts that have both a MacDonald's and a China Great Wall, assuming that there is a MacDonald's in 80% of all food courts. Solution: (c) Using the information from parts (a) and (b), compute the probability that a food court has either a MacDonald's or a China Great Wall, assuming that the presence of a Great Wall outlet is independent of the presence of a MacDonald's. Solution:

Explanation / Answer

a)

P(C|M) = 0.04 (given in question) = P(M and C)/P(M)

P(B and C) = 0.1 (given in question)

P(M|C) = P(M and C)/P(C)

= P(C/M) * P(M)/P(C)

insufficient data to calculate

P(C|M) , similarly insufficient data

P(CUM) = not enough data

P(B/C) = P(B and C) /P(C)

hence the correct choice is B

b)

P(C|M) = 0.04 = P(M and C) * P(M)

P(M and C) = P(C|M) /P(M) = 0.04/0.8 = 0.05

c)

P(M and C) =0

P(C|M) = 0.04

=>

P(C) = 0.04

P( M U C) = p(M) + P(C) + P(M and C)

= 0.8 + 0.04

= 0.84

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