Probability – The chance or likelihood that something will happen.

Probabilities must be between 0 and 1

·         A probability of 0 means it’s impossible

·         A probability of 1 means it will definitely happen

Probabilities can be expressed as…

·         Ratio

·         Fraction

·         Decimal

·         Percent

Outcome – The result of an experiment

Sample Space – All the possible outcomes of an experiment

Event – One or more outcomes of an experiment

Type of Events

1.      Independent Event – Events that is not affected by any other events.

Ex.  A coin is tossed and a single 6-sided die is rolled. Find the probability of landing on the head side of the coin and rolling a 3 on the die?

        P(head) = ½

        P(3) = 1/6

        P(head and 3) = P(head) x P(3)

                                    = (1/2) X (1/6)

                                 = 1/12

2.      Dependent Event – Events that can be affected by previous events.

Ex. A chosen is chosen at random from a standard deck of 52 cards. Without replacing it, a second card is chosen. What is the probability that the first chosen card chosen is a queen and the second card is a jack?

       P(queen on first pick) = 4/52

       P(jack on 2^nd pick given queen on 1^st pick) = 4/51

       P(queen and jack) = (4/52) x (4/51)

                                      = 16/2652

                                      = 4/633

3.      Simple Event – A single outcome in the sample space

Ex. What is the probability of rolling a 5?

        P(5) = 1/6

4.      Compound Events – More than one outcome in the sample space

Ex. What is the probability of rolling an even number?

       Ex. P(even) = 3/6

                           = 1/2

Factorial – The result of multiplying a series of decreasing numbers

Note: The factorial for 0 is always 1

Ex. 9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362 880

Ex. 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720