MATH question to answer

Question

There are 3 urns containing coins. Urn I contains 3 gold coins, urn II contains 1 gold coin and 1 silver coin, and urn III contains 2 silver coins. An urn is selected and a coin is drawn from the urn. If the selected coin is gold, what is the probability that the urn selected was urn I? (Enter your probabilities as fractions.)

(a) Use a probability tree to find the probability.

(b) Use Bayes' formula to find the probability.

Answer 1

Urn I has 3 gold, Urn II 1 gold 1 silver, Urn 3 has 2 silver

select an Urn randomly, if the coin is gold what is probability it came from Urn I?

off hand guess is 75%= 3/4 chance as 3 out of 4 of the gold coins are in Urn I

Use Bayes theorem find Pr(I/g)

Pr(g/I)P(I) = P(I/g)P(g)

Pr(I/g) = Pr(g/I)P(I)/Pr(g) = 100%(1/3)/(3/4) = (1/3)(4/3)=4/9 = 44 4/9 %, so wild guess was off a bit