Chapter-15
Probability
1. Introduction
2. Probability – an experimental approach
3. Summary
Real life connections:1. All the games on casino are played on the basis of probability.
2. The important application is reliability, many consumer products, such as automobiles &
consumer electronics, use reliability theory.
3. When your team has a coin toss before the game, you have 50-50 chances of winning it:
either heads or tails.
4. Meteorologists predict natural disasters such as earthquakes & tsunamis by applying
principles of probability bases upon patterns that have occurred in previous years.
5. Loan companies may decide to sanction a loan based on an individuals credit history to
understand how likely he is to return the many, is done asking probability.
Q.
Eleven bags of wheat flour, each marked 5kg, actually contained the
following weight of flour (in kg):
4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00
Sol:
Find the probability that any of these bags chosen at random contains
more than 5 kg of flour.
Number of bags containing more than 5 kg of flour (A) = 7
Total number of bags = 11
 PA  
7
11
( Probability of an event =
Q.
Favourable outcomes
)
Total number of outcomes
Following table shows the birth month of 40 students of class IX.
Jan
3
Sol:
Feb
4
Mar
2
Apr
2
May
5
Jun
1
July
2
Aug
6
Sept
3
Find the probability that a student was born in august.
Total number of students = 40
Number of students born in august (A) = 6
 PA  
6
3

40 20
i.e. PA  
3
20
( Probability of an event =
Favourableoutcomes
)
Total number of outcomes
Oct
4
Nov
4
Dec
4
Q.
The following table gives the life time of 400 neon lamps:
Life time (hours)
Number of lamps
300-400
14
400-500
56
500-600
60
600-700
86
700-800
74
800-900
62
900-1000
48
A lamp is selected at random. Find the probability that the life time of the
selected lamp is :-
a.) Less than 400 hours.
b.) Between 300 to 800 hours.
c.) Atleast 700 hours.
Sol:
Total number of lamps = 400
Number of lamps having life time less than 400 hours (A) = 14
Number of lamps having life time between 300 to 800 hours
(B)  14  56  60  86  74 = 290
Number of lamps having life time at least 700 hours(C)  74  62  48  184
 P(A) 
14
7

400 200
PB 
PC 
290 29

400 40
184 46 23


400 100 50
Favourbale outcomes 

 Pr obability of an event 

Total number of outcomes 
