**Probability and Permutations**

**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.

**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?

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?

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?

**Solution** :

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: