A random experiment consists of throwing 10 fair dice, each die having six faces numbered 1 to 6. An event A represents the set of all outcomes where at least one of the dice shows a 1. Then P(A) = A. 0 B. (1/6)^10 C. 1 - (5/6)^10 D. (5/6)^10

GATE 2025 · Engineering Mathematics · Classical Probability and Complementary Counting · medium

Answer: P(A) = 1 - (5/6)^10 [Option C]

1. Identify complement event A^c: A^c = event that none of the 10 dice shows 1. P(A) = 1 - P(A^c).
2. Compute P(A^c) using independence: Each die avoids 1 with probability 5/6. P(A^c) = (5/6)^10.
3. Compute P(A): P(A) = 1 - (5/6)^10 ≈ 1 - 0.1615 = 0.8385.