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GATE DA 2025 Q45: 100 dice: probability that at least one shows 1

Question

A random experiment consists of throwing 100 fair dice, each die having six faces numbered 1 to 6. An event AA represents the set of all outcomes where at least one of the dice shows a 1. Then, P(A)=P(A) =

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Answer: C (official GATE 2025 final answer key)

Concept used: Complement rule for "at least one" events with independent trials.

First step: The complement is "no die shows 1". Each die avoids 1 with probability 56\frac{5}{6}, independently.

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Source: official GATE 2025 DA question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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