Probability

Sample space - is the set of all possible outcomes of an experiment.

Tree diagrams are ordered pairs are often use to list samples space.

The probability that a specific event will occur can be described as P(E)=success / sample space.

Example 1

a. Tossing 3 coins

b. Rolling a pair of 6 sided dice.

Sample Space = 36





Example 2

A box contains 13 orange marbles and 10 green marbles.If one marble is drawn, what is the probability it will be orange?

P(orange marble) =     success    
                               sample space

P(orange marble) = 13
                                 23



Probability of Independent and Dependent Events


Complementary Events - are mutually exclusive and their sum exhaust the sample space
 ex. Tossing a coin and rolling a die.


Independent Events - two events occurs so that neither one effects the probability of the others.
 ex. Drawing two cards from a deck without replacement

Example 1: Comparing Independent and Dependent Events

You randomly select two marbles from a bag contains 14 green, 7 blue and 9 red marbles. What is the probability that the first marble is blue and the second marble is not blue if:

a. You replace the first marble before selecting the second

b. You do not replaced the first marble

Example 2

A single card is drawn from deck of 52 cards. What is the Probability that it is either Ace or Jack?