(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A stack of cards consists of six red and five blue cards. A second stack of cards consists of nine red cards. A stack is selected at random and three of its cards are drawn. If all of them are red, what is the probability that the first stack was selected?

2. Relevant equations

let X be the event of drawing three red cards, A be the first deck and B the second.

then P(A) = P(B) = .5

P(X|A) = (6/11 * 5/10 * 4/9) = .121212

P(X|B) = 1

3. The attempt at a solution

P(X|A)P(A) / [P(X|A)P(A) + P(X|B)(B)] = (.1212 * .5) / [(.1212 * .5) + (1 * .5] = .195

I think I did this right. Can anyone confirm or give me a hint as to what might be wrong? Intuitively the 1/5 answer bothers me since it seems to me that the chance of choosing one of the two decks seems like it would still be 1/2 since drawing three red cards does not imply one deck or the other, but the chapter is on Bayes' Formula and not on independence.

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# Homework Help: Bayes' formula probability problem

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