If two dice are rolled, what is the probability that the sum is 7?

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Question: If two dice are rolled, what is the probability that the sum is 7?

Options:

Correct Answer: 5/36

Solution:

Possible combinations for sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 combinations. Total outcomes = 36. Probability = 6/36 = 1/6.

If two dice are rolled, what is the probability that the sum is 7?

If two dice are rolled, what is the probability that the sum is 7?

Step 1: Understand that when two dice are rolled, each die has 6 faces, numbered from 1 to 6.
Step 2: Calculate the total number of possible outcomes when rolling two dice. Since each die has 6 faces, the total outcomes = 6 (for the first die) * 6 (for the second die) = 36.
Step 3: Identify the combinations of the two dice that add up to 7. These combinations are: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).
Step 4: Count the number of combinations that result in a sum of 7. There are 6 combinations.
Step 5: Calculate the probability of rolling a sum of 7. Probability = (Number of favorable outcomes) / (Total outcomes) = 6 / 36.
Step 6: Simplify the fraction 6/36 to get the final probability. 6/36 = 1/6.

Probability – Understanding the likelihood of an event occurring, calculated as the number of favorable outcomes divided by the total number of possible outcomes.
Combinatorics – The study of counting, arrangements, and combinations, particularly relevant in determining the total outcomes when rolling dice.