Question

You read online that the probability of being dealt four‑of‑a‑kind in a five‑card poker hand is 1/4165 1/4165 . Explain carefully what this means. In particular, explain why it does not mean that if you are dealt 4165 4165 five‑card poker hands, one will be four‑of‑a‑kind. Select the best explanation from the choices. The probability is actually saying that only on the 4165 4165 th poker hand will you get a four‑of‑a‑kind, not just on any of the 4165 4165 poker hands. The probability is actually saying that in the long run, with a large number of five‑card poker hands, the fraction in which you will be dealt a four‑of‑a‑kind is 1/4165 1/4165 . It does mean that if you are dealt 4165 4165 five‑card poker hands, one will be four‑of‑a‑kind. It does not mean that all will be four‑of‑a‑kind. The chance you will be dealt four‑of‑a‑kind is 1/4165 1/4165 only on the first hand. This chance will then increase with each new hand you are dealt until you eventually win.

Answer 1