What is the probability that the sum of two fair six-sided dice equals 7?

What is the probability that the sum of two fair six-sided dice equals 7?

• A. 1/6
• B. 1/4
• C. 1/3
• D. 1/2

Answer: (A)

Think about counting outcomes. With two fair six-sided dice there are 6 × 6 = 36 equally likely results in total. The sums that equal 7 come from six ordered pairs: (1,6), (2,5), (3,4), and their reverses (4,3), (5,2), (6,1). So the probability is 6 favorable outcomes out of 36 total, which simplifies to 1/6. The other fractions would require more favorable outcomes than actually exist for a sum of 7.

Think about counting outcomes. With two fair six-sided dice there are 6 × 6 = 36 equally likely results in total. The sums that equal 7 come from six ordered pairs: (1,6), (2,5), (3,4), and their reverses (4,3), (5,2), (6,1). So the probability is 6 favorable outcomes out of 36 total, which simplifies to 1/6. The other fractions would require more favorable outcomes than actually exist for a sum of 7.