Question

A domino is a rectangular tile composed of two squares. An integer is represented on both squares, and each integer 0-9 is paired with every integer 0-9 exactly once to form a complete set. A $\textit{double}$ is a domino that has the same integer on both of its squares. What is the probability that a domino randomly selected from a set will be a $\textit{double}$? Express your answer as a common fraction.

Answer 1

2/11

Step-by-step explanation:

There are 10C₂ possible combinations for dominoes with 2 different numbers, and there are 10C₁ possible combinations for dominoes with the same integer, or double dominoes. The probability that you select a double domino is = 10C₁ / (10C₂ + 10C₁)

where:

10C₁ = 10

10C₂ = 9 +8 +7 + 6 + 5 + 4 + 3 + 2 + 1 = 45

probability of double domino = 10 / (45 + 10) = 10/55 = 2/11