NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3
Question 26

Question. 26

Two dice are thrown. Probability that the absolute difference of the numbers is 2?

Answer:

\(\dfrac{2}{9}\)

Detailed Answer with Explanation:

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:

  • (1, 3) and (3, 1)
  • (2, 4) and (4, 2)
  • (3, 5) and (5, 3)
  • (4, 6) and (6, 4)

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 = \(\dfrac{2}{9}\).

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