A random experiment consists of throwing 100 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, \(P(A) =\)
Answer
(C)
Explanation
Use the complement: the event fails only when no die shows a 1.
Each die avoids 1 with probability \(\frac{5}{6}\), and the 100 throws are independent, so \(P(\text{no 1 at all}) = \left(\frac{5}{6}\right)^{100}\). Therefore
\[P(A) = 1 - \left(\frac{5}{6}\right)^{100}.\]
Option D is the probability of the complement. Options A and B fail because both \(A\) and its complement can happen, so \(P(A)\) lies strictly between 0 and 1, though very close to 1.
Answer: C