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

There are three identical cards that differ only in color. Both sides of one are black, both sides of the second are red, and one side of the third card is black and its other side is red. These cards are mixed up and one of them is selected at random. If the upper side of this card is red, what is the probability that its other side is black?

2. Relevant equations

A is upper red, Y is lower black

P(A) = 3/6

P(Y) = 3/6

I did 3/6 because I considered 3 sides are red and 3 are black, but this keeps nagging at me like I am missing something.

3. The attempt at a solution

P(Y|A) = P(A|Y)P(Y) / [P(A|Y)P(Y) + P(A|Yc)P(Yc)] =

1/3 * 3/6 / [1/3 * 3/6 + 1/3 * 3/6] = .5

I believe this is right, but it almost seems to be too easy to get to this without using Bayes' formula at all, but that might just be a coincidence due to the easy numbers being manipulated. Thanks for any help

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# Homework Help: Another Bayes' formula problem

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