NCERT Class 9 Maths Lab Manual – Find Probability of each Outcome or a Die

NCERT Class 9 Maths Lab Manual – Find Probability of each Outcome or a Die

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

Materials Required

1. Notebook
2. A fair die
3. Pen

Prerequisite Knowledge
Basic knowledge of probability and a fair die.

Theory

1. For basic knowledge of probability refer to Activity 33.
2. A fair die is small cube having dots, 1 to 6 on its faces.
   

Procedure

1. Firstly, divide the whole class in ten groups, say G₁, G₂, G₃, …….., G₁₀ of a suitable size.
2. Allow all groups 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. If 1 appears in all the groups a times. 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. Now, find the probability of each outcome (E) by using the formula,
   P(E) = \(\frac { Number\quad of\quad times\quad an\quad outcome\quad occurred }{ Total\quad number\quad of\quad trials }\)

Demonstration

1. There are 10 groups and all the groups throw a die 100 times. So, the total number of trials is 1000.
2. As, 1 has appeared a times.
   Hence, experimental probability of 1, P(1) = \(\frac { a }{ 1000 }\)
   similarly, experimental probability of 2, P(2) = \(\frac { b }{ 1000 }\)
   experimental probability of 3, P(3) = \(\frac { c }{ 1000 }\)
   experimental probability of 4, P(4) = \(\frac { d }{ 1000 }\)
   experimental probability of 5, P(5) = \(\frac { e }{ 1000 }\)
   and  experimental probability of 6, P(6) = \(\frac { f }{ 1000 }\)

Observations
Fill the results of your experiment in the table given below.

Outcome/Group	Number of times a number comes up on a die						Total
	1	2	3	4	5	6
G1	……	……	……	……	……	……	100
G2	……	……	……	……	……	……	100
G3	……	……	……	……	……	……	100
G4	……	……	……	……	……	……	100
G5	……	……	……	……	……	……	100
G6	……	……	……	……	……	……	100
G7	……	……	……	……	……	……	100
G8	……	……	……	……	……	……	100
G9	……	……	……	……	……	……	100
G10	……	……	……	……	……*,	……	100
Total	a = …….	b = ……..	c = …….	d = ……..	e = …..	f =…….	1000

Hence,
P(1) = \(\frac { ? }{ 1000 }\)
P(2) = \(\frac { ? }{ 1000 }\)
P(3) = \(\frac { ? }{ 1000 }\)
P(4) = \(\frac { ? }{ 1000 }\)
P(5) = \(\frac { ? }{ 1000 }\)
P(6) = \(\frac { ? }{ 1000 }\)

Result
We have got the experimental probability of each outcome of a die, when it is thrown a large number of times.

Application
The knowledge of probability is used by many statistical institutions in estimating/predicting next action based on available data.

Viva-Voce

Question 1.
How will you define the term trial?
Answer:
A trial is an action which results in one or several outcomes.

Question 2.
What is the probability of an impossible event?
Answer:
0

Question 3.
Does the sum of all the probabilities of all possible outcomes of an experiment more than 1?
Answer:
No, it is equal to 1.

Question 4.
What are the name of scientists who worked on beginning of probability theory?
Answer:
Pascal and Fermat.

Question 5.
What is the minimum probability of an event?
Answer:
0

Question 6.
What is the sum of probabilities of an event and probability of complement of an event?
Answer:
1

Question 7.
What do you mean by favourable outcomes?
Answer:
The outcomes which ensure the occurrence of an event are called favourable outcomes to the event.

Question 8.
What do you understand by a compound event?
Answer:
A collection of two or more elementary events associated with a random experiment is called compound event.

Suggested Activity
Find the experimental probability of getting an even number on a die when it is thrown a large number of times.

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