Which desk submitted the highest quote?

Question

Desk A submits 3 quotes and Desk B submits 5 quotes. All 8 quotes are drawn independently from the same continuous distribution, so ties never occur.

What is the probability that the single highest quote came from Desk A?

Accepted Answer

Pool all 8 quotes together. Because they are independent draws from the same distribution, every quote is equally likely to be the highest. Desk A owns 3 of the 8 quotes, so the probability the top quote is one of theirs is simply their share: \frac{3}{8} = 0.375. The individual quote values never enter the calculation; only the head count matters, since each of the 8 is equally likely to win. Takeaway. When several groups draw from a common continuous distribution, the overall maximum belongs to a group in proportion to that group's size.

Which desk submitted the highest quote?

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