# Problem Restatement There are **two cards** in a box: - **Card 1: Both sides red. -Card 2**: One side is red one side is green. A card is chosen at random and placed on the table. You see the **upper side is red**. **Question:** What is the probability that the chosen card is the one with both sides red? --- # Step 1: List All Sides Let’s list all possible *red sides* that could be seen: - Card 1: **Red side 1** (let’s call it R1) - Card 1: **Red side 2** (R2) - Card 2: **Red side (R3)** - Card 2: **Green side (G)** (but if you see green, you wouldn’t be in this situation) So, the possible *red sides* are: R1, R2, R3. --- # Step 2: List all Red Face-up Events When you pick a card and see a red face: - **Card 1:** You could see either R1 or R2 (both are red). - **Card 2:** You could see R3 (the red side). So, **3 ways** to see a red face: 1. Card 1, R1 up 2. Card 1, R2 up 3. Card 2, R3 up Each of these 3 ways is **equally likely**. --- # Step 3: Find the Favorable Outcomes The question asks for the probability that the card is the **both-red card** (Card 1), given that the observed side is red. From above, there are **2 ways** this happens (Card 1, R1 or Card 1, R2). --- # Step 4: Compute the Probability So, \[ P(\text{Both sides red} \mid \text{Red side up}) = \frac{\text{Number of favorable ways}}{\text{Total number of red sides up}} \] \[ = \frac{2}{3} \] --- # Final Answer **The probability that the card is the both-red card, given that the face you see is red, is \(\boxed{\frac{2}{3}}\).**