Suppose i have three cards, one with colour RED/RED on both sides, another with BLUE/BLUE on both sides and the last one with RED/BLUE on each side. drawing a random card and putting on the table i am allowed to see only the front face of the card. if a randomly drawn card appeared to be red on front face and we are unknown the another side of the card, then what is the probability that another card drawn appear to be red on the front face?
The three cards collectively have 6 faces amongst them, 3 of which are red. Two of those faces are on the completely red card, which if chosen, leave odds of 1/4 that the second card will show red. The last one is on the mixed card, which leaves a 1/2 chance that another card will show red. The answer is therefore 2/3 * 1/4 + 1/3 * 1/2 = 1/3.