COMEDK 2024 Shift 2 Paper

We have three cards with the following color configurations:
Card 1: Red on both sides.
Card 2: Black on both sides.
Card 3: Red on one side, Black on the other side.
If we pick a card at random and find that the upper side is red, we need to find the probability that the other side is black.
First, let's enumerate all possible sides of the cards:
Card 1: R, R
Card 2: B, B
Card 3: R, B
When a card is picked, any side is equally likely to be the upper side. Here are the possible outcomes where the upper side is red:
Upper side is Red, lower side is Red (Card 1, Side 1)
Upper side is Red, lower side is Red (Card 1, Side 2)
Upper side is Red, lower side is Black (Card 3, Side 1)
So, there are three possible favorable outcomes where the upper side is red. Now, we count how many of these favorable outcomes have black as the other side:
Card 1, Side 1: Other side is Red
Card 1, Side 2: Other side is Red
Card 3, Side 1: Other side is Black
Only one of these outcomes has the other side colored black. Therefore, the probability is:
Therefore, the correct answer is:
Option D
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