0 1 P(E) n(S)=6 H|T n(S)=2 ♠A n(S)=52 P(E)+P(Ē)=1 P(E)=n(E)/n(S) Face cards = 12 (not 4!) 2 dice → n(S) = 36
P(E)
Chapter 14  ·  Class X Mathematics  ·  MCQ Practice

MCQ Practice Arena

Probability

Count Favourable, Divide by Total — The Simplest Chapter with the Biggest Payoff

📋 50 MCQs ⭐ 32 PYQs ⏱ 45 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
26Easy
18Medium
6Hard
32PYQs
45 secAvg Time/Q
8Topics
Easy 52% Medium 36% Hard 12%

Why Practise These MCQs?

CBSE Class XNTSEState Boards

Probability is the highest-payoff chapter in Class X relative to study time — 6–8 Board marks achievable in 1–2 days. Every MCQ follows the same formula: P(E) = favourable outcomes / total outcomes. Problems on coins, dice, and playing cards account for 80% of questions; the patterns repeat across years. Use the complement rule to eliminate answer choices instantly.

Topic-wise MCQ Breakdown

Basic Probability Formula & Concepts6 Q
Complementary Events (P(E'))8 Q
Sample Space & Event Identification5 Q
Coin Problems8 Q
Dice Problems (Single & Double)10 Q
Playing Card Problems9 Q
Coloured Balls / Bags3 Q
Real-Life Probability (Days, Letters, etc.)1 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$P(E) = n(E)/n(S)$
$0 \le P(E) \le 1$
$P(E) + P(\bar{E}) = 1$
$P(\text{sure event}) = 1,\ P(\text{impossible event}) = 0$
$P(A\cup B) = P(A)+P(B)-P(A\cap B)$
$\text{2 dice: }n(S)=36;\ \text{deck: }n(S)=52$

MCQ Solving Strategy

List the sample space for coins and single dice immediately — it takes 10 seconds and prevents errors. For two-dice MCQs, don't list all 36 outcomes — use systematic counting (sum = 7 has 6 outcomes: (1,6),(2,5),...). For card problems, memorise: 52 cards, 4 suits (13 each), 12 face cards (J, Q, K × 4), 4 aces, 26 red, 26 black. Use complement for "at least one" questions: 1 − P(none).

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Basic formula, single coin/die, complement rule

② Medium

Cards, two-dice sums, compound event probability

③ Hard

Conditional-style logic, "at least/at most" complement problems

★ PYQ

CBSE — cards + dice; NTSE — logical probability reasoning

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 📘✔️ Exercises Step-by-step NCERT solutions ✔️❌ True / False Concept-based True & False ➡ Next Chapter Back to Chapter 1: Real Numbers
🎯 Knowledge Check

Maths — PROBABILITY

50 Questions Class 10 MCQs
1
What is the probability of getting a head when a fair coin is tossed once?
2
How many outcomes are possible when a die is thrown once?
3
What is the probability of getting an even number on a fair die?
4
What is the probability of an impossible event?
5
What is the probability of a sure event?
6
The probability of an event E is \(\frac{3}{5}\). What is the probability of its complement?
7
Which of the following is a random experiment?
8
What is the sample space when a coin is tossed once?
9
What is the probability of getting a number greater than 6 on a die?
10
Which value cannot be a probability?
11
How many cards are there in a standard deck?
12
What is the probability of drawing a red card from a deck?
13
What is meant by equally likely outcomes?
14
What is the probability of getting an odd number on a die?
15
If \(P(E)=0\), then event E is:
16
If \(P(E)=1\), then event E is:
17
What is the probability of getting tail when a coin is tossed?
18
Which event has probability \(\frac{1}{2}\)?
19
What is the probability of drawing an ace from a deck?
20
Which term represents all possible outcomes?
21
The probability of getting a prime number on a die is:
22
What is the probability of getting a black card from a deck?
23
Which is a simple event?
24
What is the probability of the sample space?
25
What is the probability of drawing a king from a deck?
26
Which probability value is correct?
27
What is the probability of getting a number less than 3 on a die?
28
What does probability measure?
29
Which is a compound event?
30
What is the probability of getting a red card that is a heart?
31
Which chapter introduces probability in NCERT Class X?
32
What is the probability of getting a number divisible by 3 on a die?
33
What is the complement of drawing a red card?
34
Which statement is true?
35
What is the probability of getting 1 when a die is thrown?
36
Which of the following is an impossible event?
37
Probability is expressed as:
38
What is the probability of getting at least one head when tossing one coin?
39
What is the probability of drawing a face card?
40
Which of the following best describes probability?
41
What is the probability of getting tail twice in two independent coin tosses?
42
Which event has the highest probability?
43
What is the probability of getting a number greater than 2 on a die?
44
Which of the following is not a random experiment?
45
What is the probability of drawing a spade?
46
Which probability value shows maximum uncertainty?
47
Probability helps in:
48
What is the probability of getting an odd number greater than 3 on a die?
49
Which method is essential before applying probability formula?
50
Why is probability studied in Class X?
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Probability | Mathematics Class 10 | Academia Aeternum
Probability | Mathematics Class 10 | Academia Aeternum — Complete Notes & Solutions · academia-aeternum.com
Multiple Choice Questions play a crucial role in mastering Probability, as they test not only formula application but also conceptual clarity, logical reasoning, and accuracy in identifying outcomes. The MCQs in this section are carefully designed to reinforce fundamental ideas such as random experiments, sample space, events, equally likely outcomes, complementary events, and the correct interpretation of probability values. These questions progress from basic understanding to exam-oriented…
🎓 Class 10 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
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Frequently Asked Questions

Probability is a numerical measure of the likelihood of an event occurring when the outcome of an experiment is uncertain.

Classical probability is defined as the ratio of the number of favourable outcomes to the total number of equally likely outcomes.

\( P(E) = \frac{\text{Number of favourable outcomes}}{\text{Total number of equally likely outcomes}} \)

A random experiment is an activity that produces one outcome from several possible outcomes, where the exact result cannot be predicted in advance.

The sample space is the complete set of all possible outcomes of a random experiment.

An event is a specific outcome or a collection of outcomes from the sample space.

Outcomes are equally likely if each outcome has the same chance of occurring.

A sure event is an event that always occurs when the experiment is performed.

The probability of a sure event is 1.

An impossible event is one that cannot occur under any circumstance in the experiment.

The probability of an impossible event is 0.

The value of probability always lies between 0 and 1, inclusive.

No, probability can never be negative.

No, probability cannot exceed 1.

The complement of an event consists of all outcomes that are not part of the event.

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    📚
    ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
    Sharing this chapter
    Probability | Mathematics Class 10 | Academia Aeternum
    Probability | Mathematics Class 10 | Academia Aeternum — Complete Notes & Solutions · academia-aeternum.com
    Multiple Choice Questions play a crucial role in mastering Probability, as they test not only formula application but also conceptual clarity, logical reasoning, and accuracy in identifying outcomes. The MCQs in this section are carefully designed to reinforce fundamental ideas such as random experiments, sample space, events, equally likely outcomes, complementary events, and the correct interpretation of probability values. These questions progress from basic understanding to exam-oriented…
    🎓 Class 10 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
    Share on
    WhatsApp
    Telegram
    X / Twitter
    Facebook
    Instagram
    Threads
    Pinterest
    LinkedIn
    Quora
    Discord
    Reddit
    Email
    academia-aeternum.com/class-10/mathematics/probability/mcqs/ Copy link
    💡
    Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

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