In the example of Applying Bayes’ Formula in Schweser. (Determining the probability that the boy reaches into the blue bag).
Now the probability of A (probability of selecting the blue bag) is 50%.
Schweser mentions that the reason that the probability of choosing the green or the blue bag is 50% since there are 20 coins in total and ten in each.
What if this wasnt the case? What if there were 5 coins in the blue bag and 15 in the green? How can the probability of picking one of two bags change? Wouldnt it be the same? 50%??
My question is the following? Is it dependent on how many coins there is in each bag?
probability of selecting a blue bag - up front is 50% - 1 out of 2 bags and you are selecting at random.
now you are trying to update probability that you selected the blue bag based on the fact that the type of coin you got was a US coin.
There is an interesting article by Scientific American on the interpretation of and developing an intuition for the Bayes theorem that you might find useful. You can find it at:
I wrote an article on Bayes’ Formula that may be of some use here: http://financialexamhelp123.com/bayes-formula/
My suggestion: draw a probability tree; it’ll make everything much, much simpler.