Probability and Permutations Topic Index | Algebra Index | Regents Exam Prep Center

 Things to remember: •  When dealing with probability and permutations, it is important to know if the problem deals with replacement, or without replacement.  For example, "with replacement" would be drawing an ace from a deck of cards and then replacing the ace in the deck before drawing a second card.  "Without replacement" would be drawing the ace and not replacing it in the deck before drawing the second card.•  Don't forget to use the counting principle for many compound events.  It is fast and easy. •  Probability formula: 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.

 Topic Index | Algebra Index | Regents Exam Prep Center Created by Lisa Schultzkie