Two dice: probability the sum is 9

Two fair dice are rolled. What is the probability that the sum of the two numbers is 9?

Step-by-step

1. Total outcomes = 6 × 6 = 36
   Two throws, 6 equally likely outcomes each
2. Outcomes summing to 9 = 4
   List the ordered pairs (1,6)(2,5)(3,4)(4,3)(5,2)(6,1)
3. 4/36 ≈ 11.11%
   Probability = favourable outcomes ÷ total outcomes

Why it works

All 36 ordered pairs of results are equally likely. The probability of a given sum is the number of pairs producing that sum divided by 36.

Common mistakes

• Forgetting the reverse pairs, such as 3+6 and 6+3.
• Assuming every sum from 2 to 12 is equally likely.

Related

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