This document defines key concepts in probability and provides examples. It discusses probability vocabulary like sample space, outcome, trial, and event. It defines probability as the number of times a desired outcome occurs over total trials. Events are independent if the outcome of one does not impact others, and mutually exclusive if they cannot occur together. The addition and multiplication rules for probability are explained. Conditional probability describes the probability of a second event depending on the first occurring. Counting techniques are discussed for finding total possible outcomes of combined experiments. Review questions are provided to test understanding of the material.

1. Probability
Vocabulary
Random Phenomenon
Sample space
Outcome
Trial
Event
Probability
Probability model
Complement
Independent
Mutually exclusive
Conditional probability
Combination
permutation

2. Key Points
 P(A)= (the number of times the desired outcome
occurs) ÷ (the total number of trials)
 Events are independent if the outcome of one
event does not influence the outcome of any
other event
 Events are mutually exclusive if they cannot
occur together
 Addition Rule: P(A or B)= P(A) + P(B) – P(A and
B)
 Multiplication Rule: If A and B are independent
events, P(A and B)= P(A)P(B)

3. Probability
 _________ is the branch of math that studies
patterns of chance
 The idea of probability is based on observation.
Probability describes what happens over
many, many trials.
 The probability, P(A), of any outcome of a random
phenomenon is the proportion of times the
outcome would occur in a long series of
repetitions.

4. Probability- terms
 In probability, an experiment is any sort of activity
whose results cannot be predicted with certainty
 The _____ _____, S, is the set of all possible
outcomes
 An _______ is one of the possible results that
can occur as a result of an experiment
 A trial is a single running or observation of a
random phenomenon
 An _____ is any outcome or set of outcomes of a
random phenomenon

5. Probability
 P(A)= (the number of times the desired outcome
occurs) ÷ (the total number of trials)
Example
 Ryan rolls the die 20 times and gets a 5 on 7 of
the rolls. Then, the probability of rolling a 5 is:
 P(A)= (the number of times you roll a 5) ÷ (the
number of times you roll the die)=
7/20

6. Experimental v Theoretical
Probability
 When a random phenomenon has k possible
outcomes that are all equally likely, then each
outcome has the probability 1/k. This is called
theoretical probability
 The actual outcome of an experimental activity is
called experimental probability

7. Probability- General Rules
 1. Probability is a number between 0 and 1.
 2. The sum of the probabilities of all possible
outcomes in a sample space is 1.
 3. The probability that an event does not occur is
1 minus the probability that it does occur. (also
called the complement of A)
 If an event has the probability of .3 of
happening, then it has a probability of .7 of not
happening( 1-0.3= 0.7)

8. Independence and Mutually
Exclusive
 Events or trials are said to be _________ if the
outcome of an event or trial doesn’t influence the
outcome of another event or trial
 Two events are ______ _______ if they cannot
occur together
 Sam can either pass the test or fail- cant do both
at same time

9. Rules of Probability- Addition

10. Rules of Probability-
Multiplication

11. Conditional Probability
Conditional probability describes the situation where
the probability of a second event is dependent upon
a first event having occurred

12. Possible outcomes and counting
techniques
 If you can do one task in A ways and a second
task in B ways, then both tasks can be done in A
x B ways.
 Flip a coin and toss a die (2)(6)= 12 possible
outcomes

13. Possible outcomes and counting
techniques

14. Possible outcomes and counting
techniques

15. Review Questions

16. Review Questions

17. Review Questions

18. Review Questions

19. Review Questions

20. Review Questions