A box contains six cards. Three of the cards are black on both sides, one card is black on one side and red on the other, and two of the cards are red on both sides. You pick a card uniformly at random from the box and look at a random side. Given that the side you see is red, what is the probability that the other side is red? Express your answer as a common fraction.
Here's my take on this
P ( Red l Red ) = P ( Red and Red )
We can disregard the three Black / Black cards [ since we already hold a Red ]
Of the three remaining cards, we had (2/3) of a chance of choosing a Red/Red card
And of the three remaining cards, we had a 5/6 chance of choosing a "Red" side showing first
So......the probability is
(2/3) / (5/6) = (2/3) (6/5) = 12 / 15 = 4 / 5