Two dice: probability the sum is 5

Two fair dice are rolled. What is the probability that the two numbers add up to 5?

Step-by-step

1. Total outcomes = 6 × 6 = 36
   Two throws, 6 equally likely outcomes each
2. Outcomes summing to 5 = 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

Two rolls give 6 × 6 = 36 equally likely ordered outcomes, and the probability is the number of favourable outcomes divided by 36. Ordered pairs such as (1,4) and (4,1) must be counted separately.

Common mistakes

• Counting unordered pairs and getting 2/36.
• Using the 11 possible sums as the denominator.

Related

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