Class 09 To find experimental probability of unit’s digits of telephone numbers listed on a page selected at random of a telephone directory.

 Activity 33 

OBJECTIVE                                                                    

To find experimental probability of unit’s digits of telephone numbers listed on a page selected at random of a telephone directory.

MATERIAL REQUIRED

Telephone directory, note book, pen, ruler.

METHOD OF CONSTRUCTION

1.   Take a telephone directory and select a page at random.

 2.    Count the number of telephone numbers on the selected page. Let it be ‘N’.

3.   Unit place of a telephone number can be occupied by any one of the digits 0, 1, ..., 9.

4.   Prepare a frequency distribution table for the digits, at unit’s place using tally marks.

5.   Write the frequency of each of the digits 0, 1, 2, ...8, 9 from the table.

6.   Find the probability of each digit using the formula for experimental probability.

DEMONSTRATION

 Prepare a frequency distribution table (using tally marks) for digits 0, 1, ..., 8, 9 as shown below:

Digit	0	1	2	3	4	5	6	7		8	9
Tally marks
Frequency	n0	n1	n2	n3	n4	n5	n6	n7		n8	n9

2.   Note down frequency of each digit (0, 1, 2, 3,...,9) from the table. Digits 0, 1, 2, 3, ..., 9 are occuring respectively n₀, n₁, n₂, n₃, ..., n₉ times. 

3.   Calculate probability of each digit considering it as an event ‘E’ using the formula

 _{P( E)=} Number of trials in which the event occured

Total number of trials

 4.   Therefore, respective experimental probability of occurence of 0, 1, 2, ..., 9 is given by 

P	(	0	)	=	n0	,	P 1 =		n1	,	P	(	2	)	=	n2	,...,	P	(	9	)	=	n9
																							N .
					N		( )		N							N
OBSERVATION
Total number of telephone numbers on a page (N) = ..........................																											.
Number of times 0 occurring at unit’s place (n0) = ........................																											.
Number of times 1 occurring at unit’s place (n1) = ........................																											.
Number of times 2 occurring at unit’s place (n2) = ........................																											.
---------------------3 -------------------------- (n3) = .........................																											.
--------------------- 4								------------------------ (n4) = .........................
Number of times 9 occurring at unit’s place																						(n9)= ........................
Therefore, experimental probability of occurence of 0																									= P(0)=	n0	= .............	,
																										N

Experimental probability of occurence of    P ( 2)= ⁿ² = ............., ...,

_.                        N

.

.

P ( 9)= ^n9/N = ............. .

APPLICATION

Concept of experimental probability is used for deciding premium tables by insurance companies, by metreological department to forecast weather, for forecasting the performance of a company in stock market.