A firm plans to test a new product in one randomly selected market area. The mar

Question

A firm plans to test a new product in one randomly selected market area. The market areas can be categorized on the basis of location and population density. The number of markets in each category is presented below. (2) 130 points] Urban (U) Total 80 50 130 Rural (R) 25 30 East (E) West (W Total 20 75 a) Find the probability that there is a market in "Rural" area b) Find the probability that there is a market in "East" OR "Urban" area. c) Given that the market is in "Rural" area, what is the probability that it is in the "East"

Explanation / Answer

(a)

P(Rural) = 75/130 = 0.5769

EXPLANATION: Total for Rural = 75. Overall Total = 130

(b)

By Addition Theorem:

P(East OR Urban) = P(East) + P(Urban) - P(East & Urban)

                         = 80/130 + 55/130 - 25/130

                           = 0.6154 + 0.4231 - 0.1923

                             = 0.8462

(c)

By Multiplication Theorem:

P(East/Rural) = P(East & Rural)/P(Rural)

                     = 55/75 = 0.7333

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