What is the probability of rolling a sum greater than 10 and a sum of 10 when rolling two number cubes?

Answer 1

To calculate the probabilities of rolling a sum greater than 10 and a sum of 10 with two number cubes (also known as dice), we need to examine the possible outcomes when rolling the dice.

1. Total Outcomes: When rolling two six-sided dice, the total number of outcomes is \(6 \times 6 = 36\).

2. Sum of 10: We need to count the pairs of rolls that give a sum of 10:

   • Possible combinations:
     • (4, 6)
     • (5, 5)
     • (6, 4)

   The pairs that sum to 10 are:

   • (4, 6)
   • (5, 5)
   • (6, 4)

   Thus, there are 3 combinations that result in a sum of 10.

3. Sum Greater than 10: Now we determine the combinations that give sums greater than 10:

   • Possible sums greater than 10 are 11 and 12.

   • For sum of 11:

     • (5, 6)
     • (6, 5)

   • For sum of 12:

     • (6, 6)

   Thus, there are 3 combinations that result in sums greater than 10.

4. Calculating Probabilities:

   • Probability of rolling a sum of 10: \[ P(\text{Sum of } 10) = \frac{\text{Number of ways to get 10}}{\text{Total outcomes}} = \frac{3}{36} = \frac{1}{12} \]

   • Probability of rolling a sum greater than 10: \[ P(\text{Sum greater than } 10) = \frac{\text{Number of ways to get greater than 10}}{\text{Total outcomes}} = \frac{3}{36} = \frac{1}{12} \]

So, the final probabilities are:

• The probability of rolling a sum of 10 is \(\frac{1}{12}\).
• The probability of rolling a sum greater than 10 is also \(\frac{1}{12}\).