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Vidaara.orgClass 7 · Mathematics
CodeVID-M07-10-EXP-01
Experimental vs Theoretical - Assignment
Chapter: Probability (Intro)
Topic: Experimental vs Theoretical Probability
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
Theoretical probability $=$
  • A.$\tfrac{\text{favourable outcomes}}{\text{total outcomes}}$
  • B.$\tfrac{\text{trials}}{\text{favourable}}$
  • C.favourable trials
  • D.total trials
2.
Experimental probability $=$
  • A.$\tfrac{\text{favourable trials}}{\text{total trials}}$
  • B.$\tfrac{\text{total}}{\text{favourable}}$
  • C.favourable outcomes
  • D.total outcomes
3.
As trials increase, experimental approaches the ___ probability.
  • A.theoretical
  • B.zero
  • C.maximum
  • D.negative
4.
A coin tossed $100$ times shows $60$ heads. $P(\text{head})$ experimental $=$
  • A.$0.4$
  • B.$0.5$
  • C.$0.6$
  • D.$1$
5.
Experimental probability is based on:
  • A.theory
  • B.experiments
  • C.guessing
  • D.opinion
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
A coin tossed $100$ times shows $60$ heads. Find the experimental $P(\text{head})$.
7.
What is the theoretical $P(\text{head})$?
8.
A die rolled $60$ times shows a $6$ ten times. Find the experimental $P(6)$.
9.
Experimental probability is based on what?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
In $200$ tosses, tails appeared $90$ times. Find the experimental $P(\text{tail})$.
11.
A die is rolled. Find the theoretical $P(\text{an even number})$.
12.
Out of $250$ bulbs, $10$ are defective. Find the experimental $P(\text{defective})$.
13.
A spinner has $4$ equal colours. Find the theoretical $P(\text{red})$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
A die is rolled $120$ times and a $6$ appears $18$ times. Compare the experimental and theoretical probabilities of a $6$.
15.
In $500$ coin tosses, heads appeared $260$ times. Find the experimental probabilities of heads and tails and comment on the theoretical value.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $\tfrac{\text{favourable outcomes}}{\text{total outcomes}}$
  2. (A) $\tfrac{\text{favourable trials}}{\text{total trials}}$
  3. (A) theoretical
  4. (C) $0.6$
  5. (B) experiments
Section B — Short Answer (2 marks)
  1. $0.6$.
  2. $\tfrac12$.
  3. $\tfrac16$.
  4. Actual experiments.
Section C — Short Answer (3 marks)
  1. $0.45$.
  2. $\tfrac12$.
  3. $0.04$.
  4. $\tfrac14$.
Section D — Long Answer (5 marks)
  1. Experimental $0.15$; theoretical $\tfrac16\approx0.17$.
  2. Heads $0.52$, tails $0.48$; both close to the theoretical $0.5$.
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