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

  • Thread starter EvilPony
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    Probability
In summary: If not, I suggest you research it. However, it is essentially saying that the probability of an event is a function of the probability of the event and the probability of the outcome. In summary, the pouch has a higher probability of containing a gold coin than a silver coin. The purse has a higher probability of containing a gold coin than a silver coin.
  • #1
EvilPony
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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 =
 
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  • #2
What have you done so far?
 
  • #3
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...
 
  • #4
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.
 
  • #5
but the 2nd one is working backwards which makes it much more difficult?
 
  • #6
The second one isn't difficult, per se, they're just making you use the formuale for conditional probabilities. :smile:

You're looking for P(silver from pouch | silver from purse) right? Well, to what is that equal?
 
  • #7
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...
 
  • #8
ok I am getting 63/64 when I do that which sounds really wrong
 
  • #9
EvilPony said:
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? :rolleyes:
 
  • #10
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?
 
  • #11
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 ?
 

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

What is the "Probability coin question"?

The Probability coin question is a famous paradox in probability theory that asks what the most likely outcome is when flipping a fair coin an infinite number of times.

What is the probability of getting heads on the first toss?

The probability of getting heads on the first toss is 50%, as the coin is fair and has two equally likely outcomes.

What is the expected number of heads in an infinite number of tosses?

The expected number of heads in an infinite number of tosses is also 50%, as each toss is independent and the probability of getting heads does not change over time.

What is the probability of getting an equal number of heads and tails in an infinite number of tosses?

The probability of getting an equal number of heads and tails in an infinite number of tosses is 0%, as it is an infinitely unlikely event.

How does this paradox challenge the concept of probability?

This paradox challenges the concept of probability by demonstrating that even with a theoretically infinite number of trials, the most likely outcome is not always the most intuitive or expected one. It highlights the importance of understanding the underlying assumptions and limitations of probability theory.

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