Question

If 𝑋 denotes the sum of the numbers appearing on a throw of two fair six-faced dice then the probability
𝑃( 7 < 𝑋 < 10) = ______ (round off to 2 decimal places).

Answer 1

Correct Answer: 0.25

Given: Two fair six–faced dice are thrown. Let the sum of numbers be \(X\). We want: \[ P(7 < X < 10) \] So the possible integer values of \(X\) are: \[ X = 8, 9 \] Total possible outcomes: Each die has 6 faces → total = \(6 \times 6 = 36\). 

---

Favourable outcomes: 

For \(X = 8\):

\[ (2,6), (3,5), (4,4), (5,3), (6,2) \] Total = **5 outcomes**

For \(X = 9\):

\[ (3,6), (4,5), (5,4), (6,3) \] Total = **4 outcomes**

Total favourable = \(5 + 4 = 9\)

---

Probability: \[ P(7 < X < 10) = \frac{9}{36} = \frac{1}{4} = 0.25 \]

Final Answer: 0.25