Two fair dice, each numbered 1 to 6, are thrown together. What is the probability that the difference between the two numbers obtained (the larger minus the smaller) is 2?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\frac{2}{9}\)
Two dice give \(6\times6=36\) equally likely ordered pairs. A pair such as (1, 3) and its reverse (3, 1) are different outcomes, so both are counted.
Number pairs that differ by 2: 1 and 3, 2 and 4, 3 and 5, 4 and 6
Each can come in either order: (1, 3), (3, 1), (2, 4), (4, 2), (3, 5), (5, 3), (4, 6), (6, 4), that is, 8 pairs
Probability \(\displaystyle =\frac{8}{36}=\frac{2}{9}\)