Assume that shoes are produced in three countries: 40 percent in Venezuela, 30 percent in New Zealand, and 30 percent in Chile. At the plant in each country, two types of shoes are made: racing shoes and training shoes. The production at each plant as allocated as shown in the table below. The shoes are randomly distributed to stores in the United States, and you purchase one pair from one of these stores. PlantRacingTrainingVenezuela0.80.2New Zealand0.30.7Chile0.550.45If you purchase a pair of training shoes selected at random, what is the probability that they were made in Venezuela?

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Asked Oct 1, 2019
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Assume that shoes are produced in three countries: 40 percent in Venezuela, 30 percent in New Zealand, and 30 percent in Chile. At the plant in each country, two types of shoes are made: racing shoes and training shoes. The production at each plant as allocated as shown in the table below. The shoes are randomly distributed to stores in the United States, and you purchase one pair from one of these stores.

 

Plant Racing Training
Venezuela 0.8 0.2
New Zealand 0.3 0.7
Chile 0.55 0.45

If you purchase a pair of training shoes selected at random, what is the probability that they were made in Venezuela?

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Expert Answer

Step 1

To work out the required conditional probability

Step 2

Required conditional probability is P(A|B) = P(A intersection B)/P(B). So, we set out to calculate the numerator and the denominator from the given data

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Let A made in Venezuela B training shoe selected P(AnB) P(made in Venezuela) xP(training shoe) =0.4x0.2 0.08

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Step 3

Now , calculate the de...

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B training shoe selected P(B) P(V)xP(training shoe from V) +P(NZ)x P(training shoe from NZ) +P(C)x P(training shoe from C) 0.4x0.2+0.3x0.7+0.3x 0.45 0.425

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