Bayes' Theorem for Probability of Drawing Coins from Pouch and Purse

[EvilPony]

A pouch has 9 gold and 3 silver coins. A purse has 9 gold and 3 silver coins. A coin is drawn at random from the pouch and put in the purse. A coin is then drawn from the purse. Enter your answers as fractions.

Given that the coin chosen from the pouch was gold, what is the probability that a gold coin was chosen from the purse?
P =

Given that a silver coin is chosen from the purse, what is the probability that a silver coin was drawn from the pouch?
P =

 

[Hurkyl]

What have you done so far?

 

[EvilPony]

well the first part I can get, just take the gold coin from the pouch and add it to the purse and then you have 10 gold coins and a total of 14 coins so the probabilty is 10/14

the 2nd part seems much more difficult, I am not even sure how to start that part...

 

[whozum]

I think they want you to consider them as two different experiments, not successive.
If you can do the first one, which looks like you can, then the second one is not much different.

 

[EvilPony]

but the 2nd one is working backwards which makes it much more difficult?

 

[Hurkyl]

The second one isn't difficult, per se, they're just making you use the formuale for conditional probabilities.

You're looking for P(silver from pouch | silver from purse) right? Well, to what is that equal?

 

[EvilPony]

is it intersection of silver from purse, silver from pouch all divided by probablity of silver from the given which would be silver from purse...

 

[EvilPony]

ok I am getting 63/64 when I do that which sounds really wrong

 

[SpaceTiger]

well the first part I can get, just take the gold coin from the pouch and add it to the purse and then you have 10 gold coins and a total of 14 coins

Am I the only one counting a total of 13 coins in the first part?

 

[jdavel]

SpaceTiger,

"Am I the only one counting a total of 13 coins in the first part?"

Nope, there's at least two of us!

Evil Pony,

What's the event space of the two draws? What's the probability of each event?

 

[Curious3141]

EvilPony, the first part is easy, although your answer is wrong because you miscounted the total number of coins after one is added to the purse.

The second part is made easier with Bayes' Theorem. Do you know this theorem ?