Is the first bid the highest of the eight?

Question

A trading desk receives 8 sealed bids, each drawn independently from the same continuous distribution, so no two are ever equal.

What is the probability that the very first bid received is the highest of all eight?

Accepted Answer

Because all eight bids come from the same distribution and are independent, every one of them is equally likely to be the largest. There is nothing special about the first bid's position, so its chance of being the top is simply \frac{1}{8} = 0.125. The continuous assumption matters only to rule out ties; with ties impossible, exactly one bid is the maximum and symmetry splits the honor evenly across all eight. Takeaway. Among n exchangeable draws, any particular one is the maximum (or the minimum) with probability 1/n, no computation required.

Is the first bid the highest of the eight?

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