Three cards in order

Topic: Random experiments and probability · more questions on this topic
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Three cards are drawn in order, without replacement, from a deck of 52. The cards are labelled 1,\ldots,52.

  1. Describe the sample space. Are the outcomes equally likely?

  2. Find the probability that the three cards are three aces.

  3. Find the probability that the three cards are one ace, one king and one queen, in any order.

  4. Find the probability that none of the three cards is an ace, king, queen or jack.

  1. \Omega is the set of ordered triples of distinct labels from 1 to 52. The draw is without replacement and no card is preferred, so the outcomes are equally likely.

  2. 4\times 3\times 2/(52\times 51\times 50).

  3. The first card may be any of the 12 aces, kings or queens, the second any of the 8 cards in the two ranks still missing, and the third any of the 4 cards in the last rank: 12\times 8\times 4/(52\times 51\times 50).

  4. There are 36 cards that are not aces, kings, queens or jacks, so the probability is 36\times 35\times 34/(52\times 51\times 50).