Scientific research on popular beverages consisted of 65 studies that were fully

Question

Scientific research on popular beverages consisted of 65 studies that were fully sponsored by the food industry, and 35 studies that were conducted with no corporate ties. Of those that were fully sponsored by the food industry, 10 % of the participants found the products unfavorable, 22 % were neutral, and 68 % found the products favorable. Of those that had no industry funding, 35 % found the products unfavorable, 18 % were neutral, and 47 % found the products favorable.

What is the probability that a participant selected at random found the products favorable?

If a randomly selected participant found the product favorable, what is the probability that the study was sponsored by the food industry?

If a randomly selected participant found the product unfavorable, what is the probability that the study had no industry funding?

Explanation / Answer

a)

If a randomly selected participant found the product favorable, what is the probability that the study was sponsored by the food industry?

Let

S = sponsored
U, N, F = unfavorable, neutral, favorable

There are 65+35 = 100 samples here.

Hence,

P(S) = 65/100 = 0.65
P(S') = 1 - P(S) = 0.35

Hence,

P(F) = P(S) P(F|S) + P(S') P(F|S') = 0.65*0.68 + 0.35*0.47 = 0.6065

Hence,

P(S|F) = P(S) P(F|S)/P(F) = 0.65*0.68/0.6065 = 0.728771641 [ANSWER]

*****************************************

b)

Here,

P(U) = P(S) P(U|S) + P(S') P(U|S') = 0.65*0.10 + 0.35*0.35 = 0.1875

Hence,

P(S'|U) = P(S') P(U|S')/P(U) = 0.35*0.35/0.1875 = 0.653333333 [ANSWER]

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