Lesson 3
Atul Roy
Please read the chapters
3
and
4
.
We are going to review
p
robability
concepts with the use of simple
examples.
Example 1.
If we roll an ordinary six faced die, what is the probability that the face with two
dots will show up?
A six faced die is a cube with 1,2,3,4,5,6 dots on the faces.
In the above phenomenon, the sample space (the set of all possible outcomes)
is
or in simple terms
{1,2,3,4,5,6}
Since there are six equally likely outcomes, and 2 dots show up in only one of
them,
P(the face with two dots will show up)
=
1
6
moreover:
P(number of dots facing up is even)
=
3
6
Example 2.
1

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
A mathematics department has 61 sections of different courses for th
is term.
Course
Number of Sections
Finite Mathematics
19
Statistics
15
Precalculus
9
Calculus I
7
Calculus II
6
Calculus III
2
Differential Equations
1
Linear Algebra
1
Abstract Algebra
1
Total=61
If a section is selected at random for evaluation,
the probability that the course is precalculus is
9
61
the probability that the course is not statistics
=
61
−
15
61
=
46
61
Example 3. Suppose that we have a group of five people
named
Alen, Bina, Chris,
David and Erin. We would like to pick a simple random sample of three people
from this group. Call the members of the group as A,B,C,D,E.
a) Let us look at the list of all possible samples
of size 3
.Theyare
ABC
ABD
ABE
ACD
ACE
ADE
BCD
BCE
BDE
CDE
b)
W
e
would like to find the probability that a sample containing Bina and
Chris is selected.
Note that there are three samples ABC, BCD, BCE containing Bina and Chris.
Therefore the probaility that a sample
with
Bina and Chris is selected is
1
10
.
2

Example 4.
If we roll two dice,
for convenience, suppose one is green and one is yellow
the possible outcomes are
or in simple terms, it is
(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)
Note that there are 36 outcomes.
If we have to calculate the probability that the sum of the dots facing up is 5
.
note that there are 4 options that give a sum of 5,
3

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*