This spinner is spun and a die is rolled at the same time. Make a table to show the possible outcomes. Find the probability that: a the spinner and the die show the same score b the score on the spinner is

To solve this problem, we need to first identify the possible outcomes of both the spinner and the die. ### Step 1: Identify the outcomes 1. **Spinner Outcomes**: Let's assume the spinner has 4 equal sections numbered 1 to 4. 2. **Die Outcomes**: A standard die has 6 faces numbered from 1 to 6. ### Step 2: Create a table of possible outcomes We can create a table where the rows represent the outcomes of the spinner and the columns represent the outcomes of the die. The table will look like this: | Spinner \ Die | 1 | 2 | 3 | 4 | 5 | 6 | |---------------|---|---|---|---|---|---| | **1** | (1,1) | (1,2) | (1,3) | (1,4) | (1,5) | (1,6) | | **2** | (2,1) | (2,2) | (2,3) | (2,4) | (2,5) | (2,6) | | **3** | (3,1) | (3,2) | (3,3) | (3,4) | (3,5) | (3,6) | | **4** | (4,1) | (4,2) | (4,3) | (4,4) | (4,5) | (4,6) | ### Step 3: Calculate the total number of outcomes The total number of outcomes is the product of the number of outcomes from the spinner and the die: \[ \text{Total Outcomes} = \text{Spinner Outcomes} \times \text{Die Outcomes} = 4 \times 6 = 24 \] ### Step 4: Find the probability that the spinner and the die show the same score The outcomes where the spinner and the die show the same score are: - (1,1) - (2,2) - (3,3) - (4,4) There are 4 favorable outcomes. The probability \( P \) that the spinner and the die show the same score is given by: \[ P(\text{same score}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{4}{24} = \frac{1}{6} \] ### Step 5: Find the probability that the score on the spinner is a specific value If we need to find the probability that the score on the spinner is, for example, 2, we can calculate it as follows: - The number of favorable outcomes for the spinner showing 2 is 6 (since it can pair with any of the die outcomes). Thus, the probability \( P \) that the score on the spinner is 2 is: \[ P(\text{spinner = 2}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{6}{24} = \frac{1}{4} \] ### Summary of Results - The probability that the spinner and the die show the same score is \( \frac{1}{6} \). - The probability that the score on the spinner is 2 is \( \frac{1}{4} \). If you have a specific value for the spinner score you want to calculate, please let me know!