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Consider the set of all possible five-card poker hands dealt fairly from a standard deck of fifty-two cards. How many atomic events are there in the joint probability distribution?

  1. 2, 598, 960
  2. 3, 468, 960
  3. 3, 958, 590
  4. 2, 645, 590
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possible poker hands

In a deck of cards there are 52 cards having 4 different suits each having 13 different ranks.

a)

In a joint probability distribution of 5 cards hand from a 52 deck of cards is calculated as shown below:

Total number of combinations possible to have a set of 5 cards from 52 is  =2598960

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 joint probability distribution that gives the probability that each of X, Y, ...

falls in any particular range or discrete set of values specified for that variable. 

pb=52C5;  

2598960

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Total atomic events or count = ⁵²C₅

= 52!/5! * (52-5)!

= 52!/5! * 47!

= (48 x 49 x 50 x 51 x 52)/5!

= 311875200/120

= 2598960

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