# Bayesian probability problem

#### martinl

##### Member
There are 2 bags. Bag A contains 100 gold coins. The other bag B contains 50 gold coins and 25 silver coins.
Suppose John chose a bag and then picked 1 coin from within, the coin was a gold coin, what's the probability
that he picked bag A ?
The answer is 0.5833 using Bayes' Theorem.

What if instead of picking only 1 coin, John picked 2 coins and both coins were gold coins. Now
what's the probability that he picked bag A ?

Does anyone know how to calculate this?

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#### Dason

##### Ambassador to the humans
Can you show how you would calculate the probability when picking just one coin?

#### Dason

##### Ambassador to the humans
Can you show how you would calculate the probability when picking just one coin?

#### martinl

##### Member
Can you show how you would calculate the probability when picking just one coin?
It's calculated in this way:
P(Bag A | gold coin) = (0.5 x 1) / (150/175)

#### Dason

##### Ambassador to the humans
Can you write out what those numbers represent. Like what formula are you plugging numbers into.

#### martinl

##### Member
Oh. The formula is like this:
P(Bag A | gold coin) = P(Bag A) x P(gold coin | Bag A) / P(gold coin)
P(Bag A) = 0.5
P(gold coin | Bag A) = 1
P(gold coin) = (150/175)