•  Don't forget to use the counting principle for many compound events.  It is fast and easy.
 

Where n(S) is the number of elements in the space and n(E) is the number of outcomes in the event.

Examples:                                                      

1.   Two cards are drawn at random from a standard deck of 52 cards, without replacement.  What is the probability that both cards drawn are queens?

event    total

the way to draw 2 cards out of a possible 4 queens     the way to draw 2 cards from a deck of 52 cards

=    4·3    =    12    =   1         52·51     2652      221

 2.   Mrs. Schultzkie has to correct papers for three different classes:  Algebra, Geometry, and  Trig.  If Mrs. Schultzkie corrects the papers for each class at random, what is the probability she corrects Algebra papers first? 

There is only one way to correct Algebra papers first.
Then, there are  ₂P₂ ways to correct the other two sets of papers. 
The "total"  -  three class sets of papers    ₃P₃ .

=      1·   2· 1    =     2     =   1               3· 2· 1           6          3

3.  A card is drawn from a deck of standard cards and then replaced in the deck.  A second card is then drawn and replaced.  What is the probability that a queen is drawn each time?

On the first draw, the probability of getting one of the four queens in the deck is 4 out of 52 cards.  Because the queen is replaced into the deck, the probability of getting a queen on the second draw remains the same.  Using the counting principle we have:

               P(draw 2 queens) = P(queen on first draw) • P(queen on second draw)

See how to use your TI-83+/TI-84+ graphing calculator  with permutations. Click calculator.