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- Homework Statement
- There are three urn contains coins

Urn 1: 5 gold coins

Urn 2: 3 gold, 3 silver

Urn 3: 3 silver

An urn is selected at randonm & a coin is drawn from the urn. If the selected coin is silver, what is the probability that urn III was selected

Determine the probability using Bayes formula & a tree

- Relevant Equations
- Bayes Formula

From my understanding of Bayes formula, it should look like something like this

[tex] P(Silver| III) = \frac{P(III | silver) \times P(silver)}{P(III)} [/tex]

now we know that P(urn III) = 1/3

and the probability of P(silver) = Pr(silver|urn I) + P(silver|urn II) + P(silver|urn III) = 1/3 (0) + 1/3 (1/2) + 1/3 (1) = 1/2

But how do i calculate P(urn 3|silver) ? Would it simply be 1/3?

If I used this, then

P(Silver| III) = (1/3)(1/2) / (1/3) = 1/2. is this correct?

Using the tree, I have attached what I believe is the right tree.

Would the answer then be P(silver| urn III) = 1/3 / (1/2) = 2/3 ?

[tex] P(Silver| III) = \frac{P(III | silver) \times P(silver)}{P(III)} [/tex]

now we know that P(urn III) = 1/3

and the probability of P(silver) = Pr(silver|urn I) + P(silver|urn II) + P(silver|urn III) = 1/3 (0) + 1/3 (1/2) + 1/3 (1) = 1/2

But how do i calculate P(urn 3|silver) ? Would it simply be 1/3?

If I used this, then

P(Silver| III) = (1/3)(1/2) / (1/3) = 1/2. is this correct?

Using the tree, I have attached what I believe is the right tree.

Would the answer then be P(silver| urn III) = 1/3 / (1/2) = 2/3 ?