6.1 Basic Probability Concept
• Definition of Probability
• Applications
• Check your understanding
Probability Vocabularies??
 Event: a group of outcomes with something in common
 Sample Space (S): The set of every possible outcomes/ events
(very general)
 A: Particular event or outcome (very specific)
 n(S): The total number of elements in the sample space(S).
 n(A): The total number of times the event A can occur.
THEN WHAT IS P(A)??.......................
What is Probability??
Probability of event A:
P(A) = n( A)
n( S )




For a particular event A, P(A) is 0≤ P(A) ≤ 1.
P(A) = 1, means the event A must occur every
time
P(A) = 0, means the event A never occurs
P(A’)= probability of A not happening
= 1- P(A)
Application 1
Question
What is the probability of
rolling
a)
an even number with
one dice?
b)
a number greater
than 3 with one dice?
Solution
The sample space for rolling one dice
is S = {1,2,3,4,5,6}. Lets say event
A is rolling an even number and B
is rolling a number greater than 3.
then, A= {2,4,6} and B= {4,5,6}
a)
1
n( A) = 3
P(A) =
=
n( S )
2
6
b)
P(B)= n(B)/n(S) = 4/6 = 2/3

Application
part
2
Question
Solution
There are three white balls
and 5 red balls in the
plastic bag. What is the
probability of choosing
a)
a white ball? (event A)
b)
two red balls? (event B)
c)
a white ball and three
red balls? (event C)

(a) There are 8C1 ways to choose
any one ball from the plastic bag.
Since there are 3 white balls,
there are 3C1 ways of choosing a
white ball. Thus,
P(A) = 3C1/ 8C1 = 3/8
(b) P(B) = 5C2 /8C2 = 5/14
(c) There are 8C4 ways of choosing 4
balls from 8. Also, there are
3C1 * 5C3 ways of choosing one white
ball and three red balls. Thus,
P(C) = (3C1 * 5C3 ) / 8C4 = 3/7
Check your understanding!!
Q.1 What is the probability of choosing a vowel from the alphabet?
(★)
Q.2 There are two dice and they are rolled simultaneously. What is
the probability of rolling (a) the same numbers, (b) the numbers
whose sum is 7 (c) the numbers whose sum is less than or
equal to 5. (★ ★)
Q.3 A dice is rolled twice. What is the probability of having the
second number that is greater than the first one? (★ ★★)
Q.4 There are 20 numbers on the board and a student is to
pick 2 of them. There are 4 winning numbers that will give the
student extra 3 marks on the test. What is the probability of
choosing 2 winning numbers? (★ ★★★)
Q.5 The set A has elements of a1, a2, a3, a4, …..,a10. If I were to
choose a subset, what is the probability of choosing the subset
that includes a1, a2, a3 ? (all three of them as a group)
(★★★★★)
LETS FIND OUT THE ANSWERS!!
Answer Key
Q.1 Among 26 alphabets, 5 of them are vowels. Therefore,
P(A) = n(A)/n(S) = 5/26
Q.2 There are 36 outcomes in total as each dice has 6 numbers.
(6C1 * 6C1). Part A: one can have (1,1), (2,2), (3,3), (4,4), (5,5), (6,6). Since
n(A)=6, the P(A) = 6/36 = 1/6
Part B: There are 6 possible ways of getting a sum of 7. Thus,
P(B) = 6/36 = 1/6
Part C: n(c) = 10 ( all the purple -coloured squares)
1 2 3 4
5
6
Thus, P(C) = 10/36 = 5/18
1
2
3
4
5
6
7
2
3
4
5
6
7
8
3
4
5
6
7
8
9
4
5
6
7
8
9
10
5
6
7
8
9
10
11
6
7
8
9
10
11
12
Q.3 Based on the chart, there are 5+4+3+2+1
outcomes for the event A. Since it involves
rolling a dice twice, n(S) = 36.
P(A) = 15/36 = 5/12
Q.4 There are 2C20 ways of picking any two
numbers from the board (n(S)). Furthermore,
the number of ways to pick two winning
numbers is 4C20 (n(A)).
P(A) = 4C2 / 2C20 = 3/95
10
First
number
Second
number
1
2,3,4,5,6
2
3,4,5,6
3,
4,5,6
4
5,6
5
6
6
--------
Q.5 The total number of subset for A is 2 . To calculate the number of subset that
includes a1, a2, a3, we calculate the number of subsets of { a4, a5, a6….a10 }, and
7
it is 2 . This is because we can add a1, a2, and a3 to each subset of { a4, a5,
a6….a10 }.
7
10
3
Therefore P(A) = 2 / 2 = 1/2 = 1/8
References
Hong, Sung Dae. Su Hack Jung Suk.
Seoul: Sung Gi, 1966.
Mathematics of Data Management,
Grade 12, (MDM4U). McGraw-Hill
Ryerson.