Talks about the theory of probability

3. ‫احتمال‬
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4. Chance plays an important part in our lives.
‫حياتنا‬ ‫في‬ ‫هاما‬ ‫دورا‬ ‫يلعب‬ ‫فرصة‬
.
‫النوع‬ ‫من‬ ‫مشاكل‬ ‫احتمال‬ ‫مع‬ ‫صفقات‬
'
‫أن‬ ‫فرصة‬ ‫هي‬ ‫ما‬
"
‫األحد‬ ‫بعض‬ ‫يحدث‬
‫اث‬
Probability deals with problems of the type
‘What is the chance that’ some event happens

5. and the answer in general will be a
numerical quantity (the probability).
‫عددية‬ ‫كمية‬ ‫تكون‬ ‫سوف‬ ‫عام‬ ‫بشكل‬ ‫والجواب‬
(
‫احتمال‬
.)

6. The word probability has different basic
meanings
‫األساسية‬ ‫مختلفة‬ ‫معاني‬ ‫لها‬ ‫الكلمة‬ ‫احتمال‬
i. A quantitative measure of uncertainty
‫اليقين‬ ‫لعدم‬ ‫كمي‬ ‫مقياس‬

7. ii. A measure of degree of belief in a
particular statement
‫خاص‬ ‫بيان‬ ‫في‬ ‫االعتقاد‬ ‫لدرجة‬ ‫مقياس‬

8. iii. Measure of chance that uncertain
event will occur
‫سيحدث‬ ‫مؤكد‬ ‫غير‬ ‫الحدث‬ ‫هذا‬ ‫فرصة‬ ‫مقياس‬

9. A probability is a numerical measure of
the chance that an event occurs .
‫حدثا‬ ‫يحدث‬ ‫أن‬ ‫فرصة‬ ‫من‬ ‫عددي‬ ‫مقياس‬ ‫هو‬ ‫واالحتمال‬

10. Chance
When a meteorologist states that the chance of rain is 50%,
the meteorologist is saying that it is equally likely to rain or
not to rain. If the chance of rain rises to 80%, it is more
likely to rain. If the chance drops to 20%, then it may rain,
but it probably will not rain.

11. Chance is how likely it is that something will
happen. To state a chance, we use a percent.
CHANCE

13. Chance
Draw a ball at random in following pouch what is the chance ball is red ?

14. Probability Questions
Zafar is the captain of his track team. The
team is deciding on a color and all eight
members wrote their choice down on equal
size cards. If Zafar picks one card at random,
what is the chance /probability that he will
pick blue?
yellow
red
blue blue
blue
green black
black

15. Sample Space
The set of all possible outcomes of a statistical
experiment is called the sample space and is usually
denoted by the letter S and the possible outcomes in S
are listed in curly brackets,
Each outcome in a sample space is called an element or
a member of the sample space, or simply a sample
point.
 

16. An event is a small part of a sample space OR an
event is a subset of a sample space. If an event
contains only one element sample point it is called
simple event otherwise it is called compound event
Event
Example

17.  
outcomes
possible
all
of
number
Total
outcomes
favourable
of
Number
Total
n
m
A
P 

If our event is denoted by A then we denote the
probability of event A occurring by P (A)
P(A) = probability of event A occurring

18. Practical Example of Probability
What is the you got in 27th night Shab e Qadar in last
Ramazan
First We required a sample space of shab e Qadar
All possible out comes
S = { 21 , 23 , 25 , 27 , 29 }
A = { 27 }
 
%
20
20
.
0
5
1
)
( 




A
P
outcomes
possible
all
of
number
Total
outcomes
favourable
of
Number
Total
n
m
A
P

19. In ludo most wanted digit 6 you start game
Question is You roll a die what is the chance
you get 6

22. All possible out comes
S = { 1 , 2 , 3 , 4 , 5 , 6 }
Favorable outcome
A = { 6 }
 
%
6
.
16
166
.
0
6
1
)
( 




A
P
outcomes
possible
all
of
number
Total
outcomes
favourable
of
Number
Total
n
m
A
P

23. Case Study
You purchase a prize bond of Rs.40000. what is the probablity
following prize bond will win first prize Rs.75,000,000

25. ABCD is a square. M is the midpoint of BC and N is the midpoint of CD. A point
is selected at random in the square. Calculate the probability that it lies in the
triangle MCN
Probability and Area
Example:

26. The blood groups of 200 people is distributed as follows: 50 have
type A blood, 65 have B blood type, 70 have O blood type and 15 have
type AB blood. If a person from this group is selected at random, what is the
probability that this person has O blood type?
Example:

27. A flywheel in a car has a spot of paint marking a point on its circumference.
The radius of the flywheel is 20 cm .A small viewing hole is provided, through
which it is possible to see 3 cm of the circumference of the flywheel.
Assuming that the mark on the flywheel is likely to be in any one position as
in any other, find the probability that when the engine is off, the mark is
visible form the viewing hole . ( 0.0239)
Example:
20 cm
3 cm

28. A terrorist has planted an armed nuclear bomb in your city and your job is to
disable it. There are 4 wires to the device. You will disable the bomb by
Cutting 2 wires, Otherwise it will explode! If the wires all look the same,
what are your chances of survival
Example:

29. A book of Electronic Analysis - I contains 732 pages numbered 1, 2, ..., 732. If
a student randomly opens the book, what is the probability that the page
number contains digit 1?
Example:

31. Prize details for Pakistan Prize Bonds Denominations are given below:
Denomin
ation
First Prize 2nd Prize 3rd Prize
No. Amount No. Amount No. Amount
Rs. 200/- 01 Rs. 750,000 05 Rs. 250,000 2,394 Rs. 1,250
Rs. 750/- 01 Rs. 1,500,000 03 Rs. 500,000 1,696 Rs. 9,300
Rs.
1,500/-
01 Rs. 3,000,000 03
Rs.
1,000,000
1,696 Rs. 18,500
Rs.
7,500/-
01 Rs. 15,000,000 03
Rs.5,000,00
0
1,696 Rs. 93,000
Rs.
15,000/-
01 Rs. 30,000,000 03
Rs.
10,000,000
1,696 Rs. 185,000
Rs.
40,000/-
01 Rs. 75,000,000 03
Rs.
25,000,000
1,696 Rs. 500,000

32. Message of the day
A small but valuable message
“A mountain is not Higher than your confidence.
Because it will by under your feet, if you reach
the top”.