Almost everyone living in Hawaii is planning on buying Girl Scout cookies. To he

Question

Almost everyone living in Hawaii is planning on buying Girl Scout cookies. To help the local troop, it is agreed that every participant will buy at least two different cookie flavors. The girl scout troop is selling three flavors of cookies: chocolate mint (CM), dulce de leche (DdL), and tomato (T). The probability that a purchase includes CM and DdL is .3, includes DdL and T is .6, includes T and CM is .3. One-third of the people who buy DdL and T also buy CM. What is the probability that someone in Hawaii didn’t order DdL flavored cookies?

Explanation / Answer

here let event of buying chocolate mint (CM), dulce de leche (DdL), and tomato (T) are CM, DdL and T

hence P(CM n DdL) =0.3

P(DdL n T)=0.6

P(T n CM) =0.3

P(CM|DdL n T)=P(CM n DdL n T)/P(DdL n T) =1/3

P(CM n DdL n T) =(1/3)*0.6 =0.2

hence P(someone in Hawaii didn’t order DdL flavored cookies) =1-P(at least one pair)

=1-P(CM U DdL U T)

=1-(P(CM n DdL)+P(DdL n T)+P(T n CM)-P(CM n DdL n T))

=1-(0.3+0.6+0.3-0.2)

=1-1 =0

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