Final answer:
The probability that the card is red when Alice draws and sees a red side is 2/3, as there are two red sides out of three possible red appearances.
Step-by-step explanation:
The question asks about the probability that the card Alice drew is red, given that she has one card that is red on both sides, one card that is black on both sides, and one card that is red on one side and black on the other. When a card is drawn, there are three possibilities for the side facing up: red from the double-red card, black from the double-black card, or red from the red/black card. Since we are considering the probability of drawing a red card, we are not concerned with the side facing down or which individual card is drawn, just that the side facing up is red.
To calculate the probability, we need to consider the total number of red sides in the mix and divide that by the total number of sides presented by the three cards. Since there are two red sides out of the six possible sides when a card is randomly drawn, the probability of drawing a red side is 2/6 or simplified as 1/3. However, if Alice looks at the card and sees a red side, the probability that the card is red (either the double-red card or the red/black card) is actually 2/3, since there are two red sides among the three potential red appearances (red/red or red/black).