Two dice are thrown. Probability that the absolute difference of the numbers is 2?
\(\dfrac{2}{9}\)
Step 1: When we throw two dice together, the total number of possible outcomes is \(6 \times 6 = 36\). So, sample space \(S = 36\).
Step 2: We need the condition: absolute difference of the two numbers is 2. That means if the first die shows \(a\) and the second die shows \(b\), then: \(|a - b| = 2\).
Step 3: Let’s list all such favourable outcomes:
So, there are 8 favourable outcomes.
Step 4: Probability = \( \dfrac{\text{Favourable outcomes}}{\text{Total outcomes}} \) = \( \dfrac{8}{36} \).
Step 5: Simplify the fraction: \( \dfrac{8}{36} = \dfrac{2}{9} \).
Final Answer: The probability = \(\dfrac{2}{9}\).