The experiment to determine Find Probability of Unit’s Digit of Telephone Numbers are part of the Class 9 Maths Lab Manual provides practical activities and experiments to help students understand mathematical concepts effectively. It encourages interactive learning by linking theoretical knowledge to real-life applications, making mathematics enjoyable and meaningful.
Maths Lab Manual Class 9 CBSE Find Probability of Unit’s Digit of Telephone Numbers Experiment
Determine Find Probability of Unit’s Digit of Telephone Numbers Class 9 Practical
Objective
To find experimental probability of unit’s digits of telephone numbers listed on a page selected at random of a telephone directory.
Materials Required
- Telephone directory
- Ruler
- Notebook
- Pen
Prerequisite Knowledge
Basic knowledge of probability.
Theory
- If E is an event that happen when an experiment is performed, then the experimental or empirical probability of the event E is given by
P(E) = \(\frac { Number\quad oftrials\quad in\quad which\quad the\quad event\quad E\quad happened }{ Total\quad number\quad of\quad trials } =\frac { n(E) }{ n(S) }\)
or
Probability of an event E = P(E) = \(\frac { Number\quad of\quad trials\quad in\quad which\quad the\quad event\quad occurred }{ Total\quad number\quad of\quad trials }\) - The probability of happening of an event always lies from 0 to 1, i.e. 0 ≤ P(E) ≤ 1.
In percentage, it lies from 0% to 100%. - If probability of an event say A is 1, i.e. P(A) = 1, then event A is called a certain event or sure event.
- If probability of an event say B is 0, i.e. P(B) = 0, then event B is called an impossible event.
- The sum of all the probabilities of all possible outcomes of an experiment is 1.
Procedure
- Taking a telephone directory, select any page at random.
- Suppose the count of total telephone numbers on the selected page is N.
- Unit place of any telephone number can be occupied by any one of the digits 0,1,2, ……. 9.
- Now, using tally marks, prepare a frequency distribution table for the digits at unit’s place.
- Now, using the table, write the frequency of each of the digits 0,1,2, …….. 9.
- By using the formula for experimental probability, find the probability of each digit.
Demonstration
1. Firstly, by using tally marks, prepare a frequency distribution table for the digits 0,1,2,…. 9
Digits | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Tally marks frequency | n0 | n1 | n2 | n3 | n4 | n5 | n6 | n7 | n8 | n9 |
2. From the table, note down the frequency of each digit from 0 to 9.
3. We get that digits 0, 1,2,…, 9 are occurring n0, n1, n2, …, n9 times respectively.
4. Considering the occurrence of each digit as an event E, the probability of event E is
P(E) = \(\frac { Number\quad of\quad trials\quad in\quad which\quad event\quad occurred }{ Total\quad number\quad of\quad trials }\)
Hence, respective experimental probability of occurrence of 0, 1, 2, …, 9 is given by
P(0) = \(\frac { { n }_{ 0 } }{ N }\), P(1) = \(\frac { { n }_{ 1 } }{ N }\), ……., P(9) = \(\frac { { n }_{ 9 } }{ N }\)
Observations
Total 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) = …………..
Number of times 3 occurring at unit’s place (n3) = ………….
Number of times 4 occurring at unit’s place (n4) = ………….
……………..
……………….
Number of times 9 occurring at unit’s place (n9) = …………….
Hence, experimental probability of occurrence of 0 = P(0) = \(\frac { { n }_{ 0 } }{ N }\)
Now, experimental probability of occurrence of 1 = P(1) = \(\frac { { n }_{ 1 } }{ N }\)
P(2) = \(\frac { { n }_{ 2 } }{ N }\)
……….
……….
P(9) = \(\frac { { n }_{ 9 } }{ N }\)
Result
We have got the experimental probability of unit’s digits of telephone numbers listed on a page selected at random of a telephone directory.
Applications
The concept of experimental probability is useful in
- deciding premium tables by insurance companies. .
- stock market to forecast the performance of a company, by metreological department to forecast weather.
Viva-Voce
Question 1.
How will you define an event?
Answer:
An event for an experiment is the collection of some outcomes of the experiment.
Question 2.
How will you define the empirical probability P(E) of an event E?
Answer:
P(E) = \(\frac { Number\quad of\quad trials\quad in\quad which\quad E\quad has\quad happened }{ Total\quad number\quad of\quad trials }\)
Question 3.
What are the maximum and minimum values of the probability of an event?
Answer:
Maximum and minimum values of the probability of an event are 1 and 0 respectively.
Question 4.
What is the complement of an event E?
Answer:
1 – P(E)
Question 5.
What is the probability of a certain event?
Answer:
1
Question 6.
How many events can occur when a coin is tossed?
Answer:
Two events, i.e. head or tail.
Question 7.
How will you define a sure event?
Answer:
If probability of an event say A is 1, i.e. P(A) = 1, then event A is called a certain event or a sure event.
Question 8.
Is the sum of all the probabilities of all possible outcomes of an experiment 1?
Answer:
Yes, the sum of all the probabilities of all possible outcomes of an experiment is 1.
Suggested Activity
Find the experimental probability of getting a tail in tossing an unbiased coin 5,10,15,20,25,30 times.
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