Probability

1
Chapter 3

• Probability

2
Section 3.1

• Events, Sample Spaces, and Probability

3
Experiment

• An experiment is an act or process of observation
  that leads to a single outcome that cannot be
  predicted with certainty.

4
Sample Point

• A sample point is the most basic outcome of an
  experiment.

5
Sample Space

• The sample space of an experiment is the
  collection of all the sample points.

6
Venn diagram

• A Venn Diagram is a pictorial method for
  presenting the sample space.
• Venn Diagram Demo

7
Counting Principle

• If you can do experiment 1 in m ways and
  experiment 2 in n ways, then you can do both
  experiments in mn ways.

8
Tree Diagram

• A tree diagram is a pictorial method of listing
  all sample points.
• Definitions
• With replacement- when an
• object is selected and it can be
• selected again.
• Without replacement an
• object cannot be selected again.
• Demo Tree Diagram

9
Probability of a Sample Point

• The probability of a sample point is the total
  number of times the sample point occurs divided
  by the total number of outcomes in the experiment.

10
Probability Rules for Sample Points

• All sample point probabilities must lie between 0
  and 1 inclusive.
• All sample point probabilities within a sample
  space must sum to 1.

11
Event

• An event is a specific collection of sample
  points.

12
Probability of an Event

• The probability of event A is the number of times
  event A occurs divided by the total number of
  outcomes. The symbol for the Probability of Event
  A is P(A)

13
Mutually Exclusive ( disjoint)

• Two events are mutually exclusive when they
  cannot occur at the same time.

14

• P(A)P(not A) 1
• P(at least one) P(none)1

15
Problem 3.1 - Page 117

• An experiment results in one of the following
  sample points A, B, C, D, or E
• P(A).1 P(B).2 P(C)? P(D) .1 P(E).1
• P(A)P(B)P( C ) P(D)P(E)1
• Answer P( C )

16
Problem 3.3 - Page 117

• The sample space for an experiment contains 5
  sample points (1,2,3,4,5)
• P(1).05
• P(2) .20
• P(3) .30
• P(4) .30
• P(5) .15
• Event A either 1,2,or 3 occurs
• P(A) ?
• Event B 1,3,or 5 occurs
• P(B) ?
• Event C 4 does not occur
• P( C ) ?

17
Problem 3.8 Page 117

• Two marbles are drawn at random and without
  replacement from a box containing two blue
  marbles and three red marbles. Determine the
  probability of observing each of the following
  events.
• Event A two blue marbles are drawn
• P(A)?
• Event BA red and a blue marble are drawn.
• P(B) ?

18
Problem 3.16 Page 118

• The maximum score possible on the Standardized
  Admission Test (SAT) is 1600. According to the
  test developers, the chance that a student scores
  a perfect 1600 on the SAT is 5 in 10,000.
• A) Find the probability that a randomly selected
  student scores a 1600 on the SAT .
  _____________
• B) In a recent year, 545 students scored a
  perfect 1600. How is this possible?