GATE DA 2025 Set 1 — Question 45
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Probability & Statistics → Probability → Independent Events
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Question
A random experiment consists of throwing 100 fair dice, each die having six faces numbered 1 to 6. An event represents the set of all outcomes where at least one of the dice shows a 1. Then,
Correct answer
(C) 1 - ((5)/(6))¹⁰⁰
Solution
The probability of event (at least one 1 in 100 throws) is calculated using the complement rule:For a single fair die, the probability of not getting a 1 is . Since the 100 throws are independent, the probability that none of them result in a 1 is:Thus, the probability of at least one 1 is:This matches option (C).
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