If two dice are rolled, what is the probability that the sum is greater than 10?

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Question: If two dice are rolled, what is the probability that the sum is greater than 10?

Options:

Correct Answer: 1/6

Solution:

The combinations for a sum greater than 10 are (5,6), (6,5), (6,6), giving a probability of 3/36 = 1/12.

If two dice are rolled, what is the probability that the sum is greater than 10?

If two dice are rolled, what is the probability that the sum is greater than 10?

Step 1: Understand that when two dice are rolled, each die has 6 faces, so there are a total of 6 x 6 = 36 possible outcomes.
Step 2: Identify the sums that are greater than 10. The possible sums greater than 10 are 11 and 12.
Step 3: List the combinations of dice rolls that give a sum greater than 10.
Step 4: For a sum of 11, the combinations are (5,6) and (6,5).
Step 5: For a sum of 12, the only combination is (6,6).
Step 6: Count the total combinations that give a sum greater than 10. There are 3 combinations: (5,6), (6,5), and (6,6).
Step 7: Calculate the probability by dividing the number of successful outcomes (3) by the total number of outcomes (36).
Step 8: The probability is 3/36, which simplifies to 1/12.

Probability – Understanding how to calculate the likelihood of an event occurring based on the total number of possible outcomes.
Combinatorics – Identifying and counting the favorable outcomes that meet the criteria of the problem.
Dice Rolling – Recognizing the possible outcomes when rolling two six-sided dice and how they can be summed.