Each time an experiment such as one toss of a coin, one roll of a dice, one spin on a spinner etc. is performed, the result is called an ___________. Theoretical Probability is a measure of what you ________ to occur. A _______________ for an experiment is the set of possible outcomes for that experiment. OUTCOME EXPECT SAMPLE SPACE

Example 1: Create a sample space for the following situation: Mr. And Mrs. Sanderson are expecting triplets. Assume there is an equally likely chance that the Sandersons will have a boy or girl. Total Number of Outcomes:

Theoretical Probability = Number of FAVORABLE outcomes in the sample space Number of TOTAL outcomes in the sample space Notation:The probability of a certain event occurring is notated by _____. Where P stands for _________ and E is the ______ occurring. probabilityevent

Example 2 - Using the sample space above, if the couple has 3 children, what is the probability of having 2 boys and 1 girl? P( of 2 boys) = P( of 3 girls) = P( of 1 boys) = P( of 2 girls) =

Example 3 - Out of 100 families with 3 children how many would you expect to have all girls? P( of 3 girls) =

The above situation is an example of an ______________ event because the outcome of one event does not affect the probability of the other events occurring. Example 4 - Radcliff is playing a game where he spins the spinner below and tosses and coin right after. Create a sample space for all possible outcomes, and then answer the questions below INDEPENDENT

Spinner Coin P(1)?P(Tails)? P(1 and Tails)?P(Even and Heads)?_______ P(5 and Tails)?P(Odd or Heads)?

Mathematically- AND means we can MULTIPLY each individual probability. OR means we can ADD the probabilities. (But don’t count an event twice!) P(Even and Heads) = P(E) x P(H) =

P(Odd or Heads) = P(O) + P(H) - P(O and H) = HW : Section 3.9pages #’s 6-29

Some probability events require the act of ____________ an item back before choosing another item. These events are called events _____________________. Other probability events require the act of _________________ an item before choosing another item. These events are called events ___________ _______________. REPLACING WITH REPLACEMENT NOT REPLACING WITHOUT REPLACEMENT

Example 1 - Suppose a bag contains 12 marbles: 6 red (R), 4 Green (G), and 2 yellow (Y). Two marbles are randomly drawn. Use a grid to find the following probabilities:

First marble returned (independent event) First marble not returned (dependent event) P(R, then R) P(R, then G) P(R, then Y) P(G, then R) P(G, then G) P(G, then Y)

First marble returned (independent event) First marble not returned (dependent event) P(Y, then R) P(Y, then G) P(Y, then Y)

CARDS A standard deck of playing cards consist of ___ cards. There are __ colors; RED and BLACK. ____ of each. There are __ suits; HEARTS, DIAMONDS, CLUBS, and SPADES. ____ of each. Each suit consist of the cards 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. __ of each.

Example 2 - Suppose you are going to pull two cards from a standard deck of 52, one right after the other WITHOUT replacing the first card. Find the following probabilities: 1.) P(A red and then a black) = 2.) P(Spade and then a Heart) =

3.) P(Jack and then an ACE) = 4.) P(2 Reds) = 5.) P(2 Kings) = HW : Section 3.9pages #’s 30-45