Class 09 To find experimental probability of each outcome of a die when it is thrown a large number of times.

 

Activity 34

OBJECTIVE	MATERIAL REQUIRED
To find experimental probability of each	Die, note book, pen.
outcome of a die when it is thrown a large
number of times.
METHOD OF CONSTRUCTION

 1.    Divide the whole class in ten groups say G₁, G₂, G₃, ..., G₁₀ of a suitable size.

 2.   Allow each group to throw a die 100 times and ask them to note down the observations, i.e., the number of times the outcomes 1, 2, 3, 4, 5 or 6 come up.

 3.    Count the number of times 1 has appeared in all the groups. Denote it by a. Similarly, count the number of times each of 2, 3, 4, 5 and 6 has appeared.

 Denote them by b, c, d, e and f respectively.

 4.   Find the probability of each outcome ‘E’ using the formula :

P(E)=

Number of times an outcome occured

 Total number of trials

 DEMONSTRATION

 1.   There are 10 groups and each group throws a die 100 times. So, the total number of trials is 1000.

 2.   Total number of times 1 has appeared is a 

Therefore, experimental probability of 1 is	P(1)=			a
	1000
Similarly, experimental probability of 2 is P(2) =		b		, of 3 is P(3) =		c		,

of 4 is	P(4)=		d	,
		1000
of 5 is	P(5)=		e	,	of 6 is P (6) =	f
		1000
					1000

OBSERVATION

 Fill in the results of your experiment in the following table: 

Outcome\			Number of times a number comes up on a die																Total
Group			1		2				3				4		5			6
G1			----		----				----				----		----			----	100
G2			----		----				----				----		----			----	100
G3			----		----				----				----		----			----	100
.			.		.				.				.		.			.
.			.		.				.				.		.			.
.			.		.				.				.		.			.
.			.		.				.				.		.			.
.			.		.				.				.		.			.
.			.		.				.				.		.			.
G10			----		----				----				----		----			----	100
Total			a = ----			b = ----			c = ----		d = ----					e = ----		f = ----	1000
Therefore,
.......					.......			.......							.......
P(1)=			, P(2)=				,	P(3)=				,	P(4)=				,
					1000										1000
1000								1000
.......					.......
P(5)=			, P(6)=				.
					1000
1000

 APPLICATION

Concept of probability is used by several statistical institutions to estimate/ predict next action based on available data.

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.