## Information Theory

author: David MacKay, University of Cambridge
published: Nov. 2, 2009,   recorded: August 2009,   views: 69767
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I have issue with the example using cards. The correct answer is 1/2. Proof:

A card is a pair of colors:

c1 = (R, R)
c2 = (R, W)
c3 = (W, W)

We choose a card (x,y) at random.

I see red, so I know x = R. He then asks P(y = R | x = R)

P(y = R | x = R) = P(x = R, y = R) / P(x = R)
= p(card = c1) / p(card = c1 or card = c2)
= p(card = c1) / (p(card = c1) + p(card = c2))
= 1 / 2

Why does he say 2/3?