Two dice: probability the sum is 10

Two fair dice are rolled. What is the probability that the two numbers add up to 10?

Step-by-step

1. Total outcomes = 6 × 6 = 36
   Two throws, 6 equally likely outcomes each
2. Outcomes summing to 10 = 3
   List the ordered pairs (1,6)(2,5)(3,4)(4,3)(5,2)(6,1)
3. 3/36 ≈ 8.33%
   Probability = favourable outcomes ÷ total outcomes

Why it works

Each of the 36 ordered outcomes is equally likely, so the probability is the count of favourable outcomes over 36. A double such as (5,5) counts as one outcome only, while (4,6) and (6,4) count as two.

Common mistakes

• Counting the doubles twice and getting 4/36.
• Using 11 or 12 as the denominator.

Related

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