Statistic Probability

Question

A roaming band of adventurers purchases potions from three guilds: 55% from guild 𝐺1G1, 30% from guild 𝐺2G2, and 15% from 𝐺3G3. Suppose 12% of the potions from guild 𝐺1G1 are cursed, 25% of potions from 𝐺2G2 are cursed, and 5% of potions from 𝐺3G3 are cursed.

Part A)

What is the probability that a potion purchased by our adventurers is cursed?

Do NOT round your answer.

Part B)

If a potion turns to indeed carry a terrible curse, what is the probability that it came from guild 𝐺2G2? Do NOT round your answer.

Answer 1

A) percent cursed is the weighted average of the percent cursed from each guild weighted by the fraction from each guild:

fraction cursed = .55*.12 + .3*.25 + .15*.05

B) Use Bayes' Law P(G2|C) = P(C|G2)P(G2)/P(C) The denominator is from part A P(C|G2) = .25 and P(G2) = .3

Another way to think of it is to calculate the fraction of the cursed that come from G2.