When learning about probability, Alex, Brian and Charles were asked the following question:

Choose 3 numbers uniformly at random: \(a_1, a_2, a_3 \sim [0,1] \). What is the probability that \(a_1\) is greatest?

They gave the following answers:

Andy: \(a_1 \) is either the greatest or not the greatest. Hence the probability is \( \frac{ \text{ positive outcomes}} { \text{ total outcomes} } = \frac{1}{2} \).

Brian: One of \(a_1, a_2, a_3 \) is the greatest. Hence the probability is \( \frac{ \text{ positive outcomes}} { \text{ total outcomes} } = \frac{1}{3} \).

Charles: \( a_1\) is either greater or less than \( a_2 \) with probability \( \frac{1}{2} \). Similarly, \( a_1 \) is either greater or less than \( a_3 \) with probability \( \frac{1}{2} \). Hence, \( a_1 \) is greater than \(a_2\) and \( a_1 \) is greater than \( a_3 \) with probability \( \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \).

Who is correct?

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