Which urn holds the smallest ticket?

Question

Urn A holds 2 tickets and Urn B holds 3 tickets. Each ticket carries an independent random value from the same continuous distribution, so no two values tie.

What is the probability that the smallest value of all five tickets is in Urn A?

Accepted Answer

Pool all 5 tickets. They are exchangeable, so each is equally likely to hold the smallest value, just as each is equally likely to hold the largest. Urn A owns 2 of the 5 tickets, so the minimum sits in Urn A with probability \frac{2}{5} = 0.4. Takeaway. The minimum, like the maximum, belongs to a group in proportion to that group's size; extremes do not favor larger or smaller values by group.

Which urn holds the smallest ticket?

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