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Three brands of cold medicine for Infants are stacked on a drug store's shelves

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Question

Three brands of cold medicine for Infants are stacked on a drug store's shelves in roughly equal amounts, but in locations with different accessibility and visual observability. The three brands were recently studied by an independent medical research organization using multiple clinical trials on infants to determine the likelihood that these medications would cause an unsafe rise in the blood pressure of infants. Brand D was shown to cause this problem about 20% of the time these controlled tests. Brand T was shown to cause the problem about 10% of the time; and Brand R's medication was shown to cause the problem 40% of the time. We know from actual computerized records from the drug store sales of these three products that Brand T is purchased twice as often as Brand D; and that Brand R is purchased about two-thirds as often as Brand D.

a) What is the probability that a bottle of cold medicine purchased at this drug store will cause an unsafe rise in the blood pressure of infants?

b) A local newspaper has reported that a nearby hospital has reported a case of unsafe rise in the blood pressure of an infant brought to the emergency room (without naming the Brand of Cold Medicine or the manufacturer). The have indicated that the Cold Medicine suspected of causing the problem was purchased at the particular drug store that we are referencing. What is the probability that the Brand of Cold Medicine is Brand D? Brand T? Brand R?

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Three brands of cold medicine for Infants are stacked on a drug store's shelves

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