1. PPT. ON INTRODUCTION TO THE
THEORY OF PROBABILITY
By: SUKHDEEP SINGH

2. Exp. :- VErify somE of law of probability
by throwing of similar coin likE objEct.
Apparatus:- A few identical coin, a plastic smooth mug, a wooden tray.
Record:- With one coin
Number of throw N = 100.
Number of coin n = 1.
(Make the record as shown)
Result:-
Number of time heads up = h = 54
Probability of getting head up =1/2
No. of times head should be up theoretically= 50
Percentage variation = (100-h)/100*50 = 23
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 … 98 99 100
Heads
up
H H H H H H H H … … T T
Tails
up
T T T T T T … … H

3. With TWO coins:-
No. of throws = N =100.
No. of coins = n= 2.
(Make the record as shown)
Result :- Exp. Count of h,h = A = 13
Exp. Count of t,t = B = 32
Exp count of h,t = C = 55
Theoretical prob. Of h,h or h,t = 0.25
No. of trials are throws =100
.’. Theoretical prob. = 100 * 0.25 =25
Percentage deviation for h,h = (25-A)/25*100 = 48
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 … 98 99 100
HH hh … … … hh
TT tt tt tt tt … … … tt
HT ht ht ht ht ht ht ht ht ht … … …

4. No. of tails = 100
.’. Theoretical prob. = 100 * 0.5 =50
Percentage deviation = (50-C)/25 *100 = 20
With any no. of coins:-
No. of throws N =100
No. of coin n =10
(Make the record as shown)

5. Graph:-
Draw a graph between expected freq. and r.

6. Result:-
Examine the deviation in each case. It is observed that as the no. of
trials is increased, the deviation goes on falling.
From the observation made above, it is possible to make following
conclusion:
1.With one coin the no. of times we get head up is nearly the same
as the expected value given by the product of the total throws and
probability of heads up i.e. N*P(h). This prove the principle of a
priori prob.
2. With two coin system
No. of times of hh + no. of times of tt + no. of times of ht is always
equal to total no. of trials.
No. of times the head of both are up i.e. n(h,h) is nearly equal to the
product of total no, of throws and the prob. of the heads being up or
N*P(hh).
3.With large no. of coins the actual frequency obtained exp. For diff.

7. Result:-
Examine the deviation in each case. It is observed that as the no. of
trials is increased, the deviation goes on falling.
From the observation made above, it is possible to make following
conclusion:
1.With one coin the no. of times we get head up is nearly the same
as the expected value given by the product of the total throws and
probability of heads up i.e. N*P(h). This prove the principle of a
priori prob.
2. With two coin system
No. of times of hh + no. of times of tt + no. of times of ht is always
equal to total no. of trials.
No. of times the head of both are up i.e. n(h,h) is nearly equal to the
product of total no, of throws and the prob. of the heads being up or
N*P(hh).
3.With large no. of coins the actual frequency obtained exp. For diff.