1. Theoretical Probability Goal: to find the probability of an event using theoretical probability.

2. Probability  A probability experiment is an activity in which results are observed. Each observation is called a trial, and each result is called an outcome. The sample space is the set of all possible outcomes of an experiment.

3. An Event…  An event is any set of one or more outcomes.  The probability of an event, written P(event), is a number from 0 (or 0%) to 1 (or 100%) that tells you how likely the event is to happen.  A probability of 0 means the event is impossible, or can never happen.  A probability of 1 means the event is certain, or has to happen.  The probabilities of all possible outcomes in the sample space add up to 1.

4. Theoretical probability  Theoretical probability is used to estimate probabilities by making certain assumptions about an experiment.  The assumption is that all outcomes that are equally likely, that is, they all have the same probability.  To find theoretical probability: number of outcomes in the event total possible outcomes

5. Example #1:  An experiment consists of rolling a fair die. There are 6 possible outcomes: 1, 2, 3, 4, 5, and 6.  What is the probability of rolling a 3, P(3)?  What is the probability of rolling an odd number, P(odd number)?  What is the probability of rolling a number less than 5, P(less than 5)?

6. Example #2:  An experiment consists of rolling one fair die and flipping a coin.  Show a sample space that has all outcomes equally likely.

7.  What is the probability of getting tails, P(tails)?  What is the probability of getting an even number and heads, P(even # and heads)?  What is the probability of getting a prime number, P(prime)? 1H2H3H4H5H6H 1T2T3T4T5T6T

8. Example #3:  Using the spinner, find the probability of each event.  P(spinning A)  P(spinning C)  P(spinning D)

9. Example #4:  Suppose you roll two fair dice and are considering the sum shown.  Since each die represents a unique number, there are 36 total outcomes.  What is the probability of rolling doubles?  There are 6 outcomes of rolling doubles: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), and (6, 6).  P(double) =

10. Example #4 cont….  What is the probability of rolling a total of 10?  There are 6 outcomes in the event “a total of 10”: (4, 6), (5, 5), and (6, 4).  P(total = 10) =  What is the probability that the sum shown is less than 5?  There are 6 outcomes in the event “total < 5” :(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), and (3, 1).  P(total < 5) =

11. Example #5: An experiment consists of rolling a single fair die.  Find P(rolling an even number)  Find P(rolling a 3 or a 5)

12. Example #6: Mrs. Rife has candy hearts in a jar. She has 27 red hearts, 16 pink hearts, and 17 white hearts.  What is the theoretical probability of drawing a white heart? A red heart?.

13. Example #7: Find each probability.  P(white)  P(red)  P(green)  P(black)  What should be the sum of the probabilities? Is it true?

14. Example #8: Three fair coins are tossed: a penny, a dime, and a quarter. Copy the table and then find the following  P(HHT)  P(TTT)  P(0 tails)  P(1 tail)  P(2 heads)  P(all the same) PennyDimeQuarterOutcome HHHHHH HHTHHT HTHHTH HTTHTT THHTHH THTTHT TTHTTH TTTTTT

15. Example #7: Find each probability.  P(white)  P(red)  P(green)  P(black)  What should be the sum of the probabilities? Is it true?