According to a market research about customer\'s shopping habits. 6.0% of popula

Question

According to a market research about customer's shopping habits. 6.0% of population like buying organic food. Of those who like buying organic food, 90.0% also like buying whole-wheat bread; of those who do not like organic food, only 25.0% like buying whole-wheat bread. Answer the following questions. a). If a person Ls randomly selected in the population, what is the chance that she likes buying organic food and whole-wheat bread? b). If a person Ls randomly selected in the population, what is the chance that she likes buying whole-wheat bread? c). If a person is randomly selected and Ls discovered to like buying whole-wheat bread, what is the chance that she likes buying organic food?

Explanation / Answer

let probabilty of buying organic food=P(Or) =0.06

of buying whole wheat bread =P(W)

hence from above P(W|Or) =0.9

P(W|Orc)=0.25

a) probabilty of buying organic food and whole wheat bread =P(Or)*P(W|Or) =0.06*0.9=0.054

b) probability of whole wheat bread=P(W)=P(Or)*P(W|Or)+P(Orc)*P(W|Orc)=0.06*0.9+0.94*0.25=0.289

c)probability of buying organic food given likes whole wheat bread =P(Or|W)=P(Or)*P(W|Or)/P(W)=0.06*0.9/0.289

=0.186851

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