Two dice: probability the total is 7

Two fair dice are rolled. What is the probability that the two numbers add up to 7?

Step-by-step

1. Total outcomes = 6 × 6 = 36
   Two throws, 6 equally likely outcomes each
2. Outcomes summing to 7 = 6
   List the ordered pairs (1,6)(2,5)(3,4)(4,3)(5,2)(6,1)
3. 6/36 ≈ 16.67%
   Probability = favourable outcomes ÷ total outcomes

Why it works

There are 6 × 6 = 36 equally likely ordered outcomes. Exactly 6 of them sum to 7, so the probability is 6/36.

Common mistakes

• Counting unordered pairs and getting 3/36.
• Using 12 or 11 as the denominator.

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