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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-15-EMP-01
Empirical Probability - Assignment
Chapter: Probability
Topic: Experimental (Empirical) 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.
Empirical probability $=$
  • A.$\tfrac{\text{favourable trials}}{\text{total trials}}$
  • B.$\tfrac{\text{total}}{\text{favourable}}$
  • C.favourable trials
  • D.total trials
2.
Empirical probability is based on:
  • A.theory
  • B.actual experiments
  • C.guessing
  • D.opinion
3.
A coin tossed $100$ times shows $60$ heads. $P(\text{head})=$
  • A.$0.4$
  • B.$0.5$
  • C.$0.6$
  • D.$1$
4.
As trials increase, empirical probability approaches the ___ probability.
  • A.theoretical
  • B.zero
  • C.maximum
  • D.negative
5.
The empirical probability of an event can be at most:
  • A.$0$
  • B.$0.5$
  • C.$1$
  • D.$2$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Write the formula for empirical probability.
7.
A die is rolled $50$ times; a $6$ appears $8$ times. Find $P(6)$.
8.
A coin is tossed $200$ times, giving $90$ tails. Find $P(\text{tail})$.
9.
Empirical probability is found from what?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
In $500$ tosses, heads appeared $245$ times. Find the empirical probabilities of heads and tails.
11.
A bag test: a ball is drawn (with replacement) $80$ times; red appears $32$ times. Find $P(\text{red})$.
12.
A die rolled $120$ times gives an even number $66$ times. Find $P(\text{even})$.
13.
Out of $250$ bulbs tested, $10$ were defective. Find the empirical probability that a bulb is defective.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
A coin was tossed $1000$ times: heads $530$, tails $470$. Find both empirical probabilities and comment on how they compare with the theoretical value $0.5$.
15.
In a survey of $400$ families, $220$ had a car. Find the empirical probability that a family has a car and that it does not.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $\tfrac{\text{favourable trials}}{\text{total trials}}$
  2. (B) actual experiments
  3. (C) $0.6$
  4. (A) theoretical
  5. (C) $1$
Section B — Short Answer (2 marks)
  1. $P(E)=\dfrac{\text{number of favourable trials}}{\text{total number of trials}}$.
  2. $\tfrac{8}{50}=0.16$.
  3. $0.45$.
  4. Actual experiments/observations.
Section C — Short Answer (3 marks)
  1. $P(\text{head})=0.49$, $P(\text{tail})=0.51$.
  2. $0.4$.
  3. $0.55$.
  4. $0.04$.
Section D — Long Answer (5 marks)
  1. $P(\text{head})=0.53$, $P(\text{tail})=0.47$; both are close to the theoretical $0.5$.
  2. $P(\text{car})=0.55$; $P(\text{no car})=0.45$.
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