Drawing from 365 balls

Topic: Random experiments and probability · more questions on this topic
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Three balls are drawn from an urn of 365 balls labelled 1,\ldots,365, and the order is recorded.

  1. How many outcomes are there if each ball is replaced before the next draw?

  2. How many outcomes are there if the balls are not replaced?

  3. In the experiment with replacement, what is the probability that all three draws show the same label?

  1. Each of three ordered draws has 365 choices, so |\Omega|=365^3.

  2. Without replacement, |\Omega|=365\times 364\times 363.

  3. The first draw may be anything. The next two must match it, which has probability 1/365\times 1/365. Equivalently, 365/365^3=1/365^2.