Question

Suppose we have three cards identical in form except that both sides of the first card are coloured red, both sides of the second are coloured black, and one side of the third card is coloured red and the other side is coloured black. The three cards are mixed and a card is picked randomly. If the upper side of the chosen card is coloured red, what is the probability that the other side is coloured black?

• A. \( \frac{1}{6} \)
• B. \( \frac{1}{2} \)
• C. 0
• D. \( \frac{1}{3} \)

Hint:

When solving probability problems involving multiple outcomes, count the favorable outcomes and divide by the total number of outcomes to find the probability.

Answer 1

The Correct Option is D

We have three cards with the following configurations: 
1. First card: Both sides are red. 
2. Second card: Both sides are black. 
3. Third card: One side is red and the other side is black. 
The three cards are mixed, and one card is picked randomly. We are given that the upper side of the chosen card is coloured red. We need to find the probability that the other side is coloured black. Let’s analyze the possible cases: 
- Case 1: The chosen card is the first card (both sides red). In this case, the other side is also red. 
- Case 2: The chosen card is the third card (one side red and one side black). In this case, the other side is black. Out of the three cards, two have a red side facing up (the first and third cards). The third card is the only one where the other side is black. 
Thus, the probability that the other side is black, given that the upper side is red, is: \[ \frac{1 \text{ favorable outcome (third card)}}{3 \text{ possible outcomes (first, second, third cards)}} = \frac{1}{3} \] Thus, the correct answer is \( \frac{1}{3} \).