Two six-sided number cubes are rolled and the faces are summed. What is the probability that the sum is less than 10?

1. Two cubes give 6 x 6 = 36 equally likely outcomes. 2. It is faster to count the complement, sums of 10 or more. 3. Sum 10 comes from 4-6, 5-5, 6-4: three outcomes. 4. Sum 11 comes from 5-6 and 6-5: two outcomes, and sum 12 only from 6-6: one outcome. 5. The complement has 3 + 2 + 1 = 6 outcomes, so P(sum >= 10) = 6/36 = 1/6. 6. By the Complement Rule, P(sum < 10) = 1 - 1/6 = 5/6. 7. Option A, 1/6, reports the complement itself and forgets the final subtraction from 1. 8. Options B and C miscount the boundary, wrongly including or excluding the three ways to roll exactly 10. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.7 PROBABILITY_