**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**

- Notebook
- A fair die
- Pen

**Prerequisite Knowledge**

Basic knowledge of probability and a fair die.

**Theory**

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

**Procedure**

- Firstly, divide the whole class in ten groups, say G
_{1}, G_{2}, G_{3}, …….., G_{10}of a suitable size. - 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.
- 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.
- 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**

- There are 10 groups and all the groups throw a die 100 times. So, the total number of trials is 1000.
- 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 |
||

^{G}1 |
…… | …… | …… | …… | …… | …… | 100 |

G_{2} |
…… | …… | …… | …… | …… | …… | 100 |

^{G}3 |
…… | …… | …… | …… | …… | …… | 100 |

^{G}4 |
…… | …… | …… | …… | …… | …… | 100 |

^{G}5 |
…… | …… | …… | …… | …… | …… | 100 |

^{G}6 |
…… | …… | …… | …… | …… | …… | 100 |

^{G}7 |
…… | …… | …… | …… | …… | …… | 100 |

^{G}8 |
…… | …… | …… | …… | …… | …… | 100 |

^{G}9 |
…… | …… | …… | …… | …… | …… | 100 |

^{G}10 |
…… | …… | …… | …… | ……*, | …… | 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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