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.