Ask AI: How do you calculate the probability of rolling at least one 5 with two six-sided dice?

To calculate the probability of rolling at least one 5 with two six-sided dice, follow these steps: 1. **Determine the total number of possible outcomes:** Each die has 6 faces, so if you roll two dice, the total number of possible outcomes is: \[ 6 \times 6 = 36 \] 2. **Calculate the number of outcomes where neither die shows a 5:** If we want to count the cases where neither die shows a 5, each die has 5 other faces (1, 2, 3, 4, 6). Therefore, the total number of outcomes where no die shows a 5 is: \[ 5 \times 5 = 25 \] 3. **Calculate the number of favorable outcomes:** The favorable outcomes are the ones where at least one die shows a 5. We can find this by subtracting the number of outcomes from step 2 from the total number of possible outcomes: \[ 36 - 25 = 11 \] 4. **Calculate the probability:** The probability of rolling at least one 5 is the number of favorable outcomes divided by the total number of possible outcomes: \[ \text{Probability} = \frac{11}{36} \] So, the probability of rolling at least one 5 with two six-sided dice is \(\frac{11}{36}\).

To calculate the probability of rolling at least one 5 with two six-sided dice, we can find the probability of not rolling a 5 with any of the dice and then subtract that from 1. Probability of rolling a 5 with one die: 1/6 (since there is one 5 on a six-sided die) Probability of not rolling a 5 with one die: 5/6 (since there are five other outcomes) Now, we deal with both dice. Probability of neither die rolling a 5: (5/6) * (5/6) = 25/36 (because the two dice are independent events) Now we subtract this from 1 to find the probability of at least one die rolling a 5: 1 - 25/36 = 11/36 The probability of rolling at least one 5 with two six-sided dice is 11/36.