p q p∧q p⇒q T T T T T F F F F T F T F F F T p⇒q ≡ ¬p ∨ q Contrapositive: ¬q⇒¬p
P(E)
Chapter 14  ·  Class XI Mathematics  ·  MCQ Practice

MCQ Practice Arena

Probability

Master Uncertainty — Score Fast in Boards & Crack JEE Logic

📋 50 MCQs ⭐ 20 PYQs ⏱ 45 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
26Easy
18Medium
6Hard
20PYQs
45 secAvg Time/Q
10Topics
Easy 52% Medium 36% Hard 12%

Why Practise These MCQs?

JEE MainNEETCBSE

Probability is one of the most scoring and concept-driven chapters in Class XI Mathematics. It contributes direct MCQs in CBSE and forms a strong base for Class XII probability (conditional probability, Bayes theorem). JEE Main typically asks 1–2 straightforward questions involving classical probability, complements, or dice/card problems. Total mastery time: 3–4 hours with MCQ practice.

Topic-wise MCQ Breakdown

Basic Concepts & Terms6 Q
Sample Space5 Q
Events (Simple & Compound)5 Q
Probability Formula6 Q
Complementary Events5 Q
Dice Problems6 Q
Card Problems6 Q
Coin Problems4 Q
Axiomatic Probability4 Q
Real-Life Probability Logic3 Q

Must-Know Formulae Before You Start

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

$P(E) = n(E) / n(S)$
$0 ≤ P(E) ≤ 1$
$P(E') = 1 - P(E)$
$P(A ∪ B) = P(A) + P(B) - P(A ∩ B)$
$\text{For mutually exclusive: }P(A ∪ B) = P(A) + P(B)$
$\text{Total outcomes: Coin = }2^n, \text{ Dice }(2) = 36,\text{ Cards }= 52$

MCQ Solving Strategy

In JEE and NEET, most probability questions are direct formula-based. First identify sample space clearly. Use complement for “at least” and “not” questions. Avoid listing all outcomes unless necessary — use symmetry and counting logic. Card and dice questions are highly repetitive — memorize patterns. Always simplify fractions quickly for faster solving.

⚠ Common Traps & Errors

Difficulty Ladder

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

① Easy

Basic probability formula, coin & die questions

② Medium

Cards, complements, event classification

③ Hard

Mixed events, logical probability reasoning

★ PYQ

JEE Main — dice/cards; CBSE — definitions + numericals

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 🎯 PYQ Bank Previous year questions ✔️❌ True / False Concept-based True & False questions 📘✔️ Exercises Step by step Solutions to textbook exercises ➡ Next Chapter Back to Chapter 1: Sets MCQs
🎯 Knowledge Check

Maths — PROBABILITY

50 Questions Class 11 MCQs
1
If a fair coin is tossed once, what is the probability of getting a head?
(Board)
2
A die is thrown once. Find the probability of getting an even number.
(Board)
3
From numbers 1 to 10, one number is chosen at random. Find probability it is prime.
(Board)
4
Probability of an impossible event is:
(Board)
5
Probability of a sure event equals:
(Board)
6
If \(P(A)=\frac34\), find \(P(A')\).
(Board)
7
A card is drawn from a deck. Probability of getting a red card?
(Board)
8
Two coins are tossed. Probability of getting exactly one head?
(Board)
9
A die is thrown. Probability of getting a number greater than 4?
(Board)
10
If events \(A\) and \(B\) are mutually exclusive, then \(P(A\cap B)\) is:
(Board)
11
Probability of drawing an ace from a deck:
(Board)
12
Three coins are tossed. Probability of getting all heads?
(Board)
13
If \(P(A)=0.6\), find \(P(A')\).
(Board)
14
Probability always lies between:
(Board)
15
One card drawn. Probability it is king or queen?
(Board)
16
Two dice thrown. Probability of sum 7?
(Board)
17
Probability of at least one head in two tosses?
(Board)
18
Bag has 5 red and 3 blue balls. One drawn. Probability of blue?
(Board)
19
Probability of drawing a non-face card?
(Board)
20
Two dice thrown. Probability both even?
(Board)
21
Two dice are thrown together. Find the probability of getting the same numbers.
(Board)
22
If \(P(A)=0.4,P(B)=0.5\) and \(P(A\cap B)=0.1\), find \(P(A\cup B)\).
(Board)
23
What is the probability that a leap year has 53 Sundays?
(Board)
24
Two cards are drawn successively without replacement. Find probability that both are red.
(Board)
25
Three coins are tossed. Probability of getting exactly two heads.
(Board)
26
Two dice are thrown. Find probability that the product of numbers obtained is even.
(Board)
27
One letter is chosen at random from the word “PROBABILITY”. Find probability that it is a vowel.
(Board)
28
Three cards are drawn at random. Find probability that all are kings.
(Board)
29
If events \(A\) and \(B\) are independent, then \(P(A\cap B)\) equals:
(Board)
30
Two balls are drawn from a bag containing 3 red and 2 blue balls. Find probability both are red.
(Board)
31
Probability of at least one success in two trials when \(p=\frac12\):
(Board)
32
A card drawn is red. Find probability that it is an ace.
(Board)
33
Complement of an impossible event is:
(Board)
34
If \(P(A)=0.7\), find \(P(A')\).
(Board)
35
Two coins are tossed. Probability of getting at most one head.
(Board)
36
Two dice thrown. Probability of getting exactly one six.
(Board)
37
Three coins tossed. Probability of no tail.
(Board)
38
A card drawn. Probability it is a spade or a king.
(Board)
39
From 3 red and 2 blue balls, two reds followed by one blue are drawn without replacement. Probability?
(Board)
40
The formula for conditional probability is:
(Board)
41
Three dice thrown. Probability all show same number.
(Board)
42
One number chosen from 1 to 20. Probability it is divisible by 3.
(Board)
43
Two cards drawn with replacement. Probability both are red.
(Board)
44
Two cards drawn without replacement. Probability no ace.
(Board)
45
Two coins tossed. Probability both tails.
(Board)
46
Three coins tossed. Probability of exactly one head.
(Board)
47
Two numbers selected from 1–5. Probability both are odd.
(Board)
48
Probability of getting a prime number on a die.
(Board)
49
Two dice thrown. Probability of at least one six.
(Board)
50
If \(P(A)=0.3\) and \(P(B)=0.4\) are independent, find \(P(A\cap B)\).
(Board)
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Frequently Asked Questions

Probability is a numerical measure of the likelihood of an event, defined as \(P(E)=\frac{\text{Number of favourable outcomes}}{\text{Total number of equally likely outcomes}}\).

An experiment is a process whose outcome cannot be predicted with certainty in advance.

The sample space \(S\) is the set of all possible outcomes of an experiment.

Any subset of the sample space is called an event.

If all outcomes are equally likely, then \(P(E)=\frac{n(E)}{n(S)}\).

A random experiment is one whose result cannot be predicted with certainty but has well-defined possible outcomes.

Outcomes having the same chance of occurrence are called equally likely outcomes.

An event that always occurs has probability \(1\).

An event that never occurs has probability \(0\).

For any event \(E\), \(0\le P(E)\le1\).

If \(E\) is an event, then its complement is \(\bar E\), where \(P(\bar E)=1-P(E)\).

\(P(S)=1\).

\(P(\phi)=0\).

An event containing only one outcome is called an elementary event.

An event containing more than one outcome is called a compound event.

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