Blackjack

Date: 10/01/2003 at 22:10:41
From: Therese
Subject: Probability

If you have a standard deck of cards, what is the probability of
drawing blackjack if I draw the first two cards consecutively? 

Date: 10/03/2003 at 13:51:24
From: Doctor Ian
Subject: Re: Probability

Hi Therese,

First, write down all the ways you could get blackjack:

  king(hearts),   ace(hearts)
  king(clubs),    ace(hearts)
  king(diamonds), ace(hearts)

and so on.  Count them up.  This is the number of ways to get
blackjack by drawing two cards. 

The number of ways to get _anything_ by drawing two cards is 52*51. 
(There are 52 ways to draw the first card, and 51 ways to draw the
second.) 

The probability of getting blackjack is then

      number of ways to get blackjack
  p = -------------------------------
               52 * 51

Note that you might be able to get the numerator by being clever.  For
example, you can get blackjack by drawing a face card (or 10) and an
ace.  There are 16 ways to get a face card or 10.  And there are 4
ways to get an ace.  So there are 16*4 ways to get blackjack this way. 

What about other ways? 

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/