6. Toss a pair of dice. What is the probability that the sum is twenty or six?

To solve the problem, we need to determine the probability of rolling a sum of either 20 or 6 with a pair of dice. ### Step 1: Analyze the possible outcomes When tossing a pair of six-sided dice, the possible sums range from 2 (1+1) to 12 (6+6). Therefore, a sum of 20 is impossible with two dice. ### Step 2: Calculate the probability of rolling a sum of 6 Next, we need to find the combinations that result in a sum of 6. The possible pairs (die1, die2) that yield a sum of 6 are: - (1, 5) - (2, 4) - (3, 3) - (4, 2) - (5, 1) This gives us a total of 5 combinations that result in a sum of 6. ### Step 3: Calculate the total number of outcomes The total number of outcomes when rolling two dice is: \[ 6 \times 6 = 36 \] ### Step 4: Calculate the probability The probability \( P \) of rolling a sum of 6 is given by the ratio of the number of favorable outcomes to the total number of outcomes: \[ P(\text{sum of 6}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{5}{36} \] ### Final Answer Since a sum of 20 is impossible, the probability of getting a sum of 20 or 6 is simply the probability of getting a sum of 6: \[ P(\text{sum of 20 or 6}) = P(\text{sum of 6}) = \frac{5}{36} \] Thus, the final answer is: \[ \frac{5}{36} \]