Vidaara.orgClass 9 · Mathematics
CodeVID-M9-15-CT
Probability — Full Chapter Test
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- This is a full-length test covering the whole chapter — every topic is included.
- 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.
Probability measures the ___ of an event.
- A.cost
- B.likelihood
- C.length
- D.weight
2.
Empirical probability $=$
- A.$\tfrac{\text{favourable trials}}{\text{total trials}}$
- B.$\tfrac{\text{total}}{\text{favourable}}$
- C.favourable trials
- D.total trials
3.
$P(\text{head})$ on one coin toss:
- A.$0$
- B.$\tfrac12$
- C.$1$
- D.$\tfrac14$
4.
The probability of an event lies between:
- A.$-1$ and $1$
- B.$0$ and $1$
- C.$0$ and $100$
- D.$1$ and $2$
5.
Empirical probability is based on:
- A.theory
- B.actual experiments
- C.guessing
- D.opinion
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Between which two values does a probability lie?
7.
Write the formula for empirical probability.
8.
A die is rolled. Find $P(\text{a }5)$.
9.
What is the probability of a certain event?
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Can a probability be $1.5$? Why?
11.
In $500$ tosses, heads appeared $245$ times. Find the empirical probabilities of heads and tails.
12.
A bag has $3$ red and $5$ blue balls. Find $P(\text{red})$.
13.
Can a probability be negative?
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Explain, with the certain and impossible events as examples, why $0\le P(E)\le1$.
15.
A coin was tossed $1000$ times: heads $530$, tails $470$. Find both empirical probabilities and comment on how they compare with the theoretical value $0.5$.
Answer Key
Section A — Multiple Choice Questions
- (B) likelihood
- (A) $\tfrac{\text{favourable trials}}{\text{total trials}}$
- (B) $\tfrac12$
- (B) $0$ and $1$
- (B) actual experiments
Section B — Short Answer (2 marks)
- $0$ and $1$.
- $P(E)=\dfrac{\text{number of favourable trials}}{\text{total number of trials}}$.
- $\tfrac16$.
- $1$.
Section C — Short Answer (3 marks)
- No; probability cannot exceed $1$.
- $P(\text{head})=0.49$, $P(\text{tail})=0.51$.
- $\tfrac38$.
- No; it cannot be less than $0$.
Section D — Long Answer (5 marks)
- An impossible event has $P=0$ and a certain event has $P=1$; every other event lies between, so $0\le P(E)\le1$.
- $P(\text{head})=0.53$, $P(\text{tail})=0.47$; both are close to the theoretical $0.5$.
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