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Total of a pair

ProbabilityEasy

Roll $2$ fair $6$ -sided dice independently. What is the probability that the total equals $9$ ?

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Hint

List the ordered pairs of faces that add up to the target and divide by the number of equally likely outcomes.

Solution

There are $6 \times 6 = 36$ equally likely ordered outcomes.
The ordered pairs with total $9$ are $(3, 6)$ , $(4, 5)$ , $(5, 4)$ and $(6, 3)$ .
That gives $4$ favourable outcomes.
The probability is $\frac{4}{36}$ , which reduces to $\frac{1}{9}$ .

Answer: $\frac{1}{9}$