Mathematics Lab Activity-20 Class X | Probability

 Mathematics Lab Activity-20 Class X

Mathematics Lab Activities on Probability for class X students with complete observation tables strictly according to the CBSE syllabus.

Chapter - 14 probability

Activity - 20

Objective

To determine experimental probability of 1, 2, 3, 4, 5 or 6 by throwing a die 500 times and compare them with their theoretical probabilities.

Material Required

A fair die, pen, sheets of white paper.

Procedure

1. Divide the students of the class into ten groups I, II, III, IV, V, VI, VII, VIII, IX and X of suitable size.

2. Each group will throw a die 50 times and will observe the occurrence of each 1, 2, 3, 4, 5 and 6. as shown in figure 1

Figure 1

3. Count the total number of times (frequency) 1 comes up in each group and denote it by a₁, a₂, a₃ ,...., a₁₀, respectively. Find the sum of probabilities of getting 1 for all students.

4. Count the total number of times (frequency) 2 comes up in each group and denote it by b₁, b₂, b₃ ,...., b₁₀, respectively. Find the sum of probabilities of getting 2 for all students.

5. Count the total number of times (frequency) 3 comes up in each group and denote it by c₁, c₂, c₃ ,...., c₁₀, respectively. Find the sum of probabilities of getting 3 for all students.

3. Count the total number of times (frequency) 4 comes up in each group and denote it by d₁, d₂, d₃ ,...., d₁₀, respectively. Find the sum of probabilities of getting 4 for all students.

6. Count the total number of times (frequency) 5 comes up in each group and denote it by e₁, e₂, e₃ ,...., e₁₀, respectively. Find the sum of probabilities of getting 5 for all students.

7. Count the total number of times (frequency) 6 comes up in each group and denote it by f₁, f₂, f₃ ,...., f₁₀, respectively. Find the sum of probabilities of getting 6 for all students.

Observations & calculations 

Group No.	No. of Trials	Total number of times a number comes up
		1	2	3	4	5	6
I	50	8	9	10	11	7	5
II	50	5	7	11	9	10	8
III	50	7	11	9	10	8	5
IV	50	10	5	11	7	9	8
V	50	10	12	4	8	7	9
VI	50	8	9	11	10	5	7
VII	50	9	10	5	8	11	7
VIII	50	12	10	8	4	7	9
IX	50	5	11	7	9	8	10
X	50	10	4	8	7	9	12
TOTAL	500	84	88	84	83	81	80

Calculations of Experimental Probabilities

Sum of all probabilities of getting 1
= 84/500 = 1/6 Approximately

Sum of all probabilities of getting 2
= 88/500 = 1/6 Approximately

Sum of all probabilities of getting 3
= 84/500 = 1/6 Approximately

Sum of all probabilities of getting 4
= 83/500 = 1/6 Approximately

Sum of all probabilities of getting 5
= 81/500 = 1/6 Approximately

Sum of all probabilities of getting 6
= 80/500 = 1/6 Approximately

Theoretical Probability

When we toss a die then probability of getting each number (E) (1, 2, 3, 4, 5, 6) 

From these observations we conclude that

Theoretical Probability = Experimental Probability

Result

When we repeat an experiment to a large number of extent then Theoretical probability and experimental probability becomes equal.

Applications

Probability is used extensively in the fields like physical sciences, commerce, biological sciences, medical sciences, weather forecasting, etc.

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