NCERT Class 11 Maths Chapter 14 Probability – Concepts, Formulas, Examples & PYQs Explained

8 CBSE Marks

★★★★★ Difficulty

8 Topics

High JEE Weight

Topics Covered

8 key topics in this chapter

Random Experiment & Sample Space

Events & Types of Events

Probability of an Event

Addition Theorem

Mutually Exclusive Events

Exhaustive Events

Equally Likely Outcomes

Geometric Probability (intro)

Study Resources

📖 NCERT Notes ✏️ MCQ Practice 🏆 JEE / CBSE PYQs 📝 Exercise Solutions ✅ True / False Quiz

𝑓 Key Formulae

Essential mathematical expressions for this chapter — understand derivations, not just results.

Classical Prob.

\[P(A) = \dfrac{n(A)}{n(S)}\]

📌 n(A) = favourable outcomes, n(S) = total

Complement

\[P(A') = 1 - P(A)\]

📌 0 ≤ P(A) ≤ 1 always

Addition Rule

\[P(A\cup B) = P(A)+P(B)-P(A\cap B)\]

📌 Inclusion-exclusion for probability

Mutually Excl.

\[P(A\cup B) = P(A)+P(B)\quad\text{if }A\cap B=\emptyset\]

📌 No overlap between events

Three Events

\[P(A\cup B\cup C)=P(A)+P(B)+P(C)-P(A\cap B)-P(B\cap C)-P(A\cap C)+P(A\cap B\cap C)\]

📌 Extension of addition rule

Odds in Favour

\[\text{Odds} = \dfrac{P(A)}{1-P(A)} = \dfrac{P(A)}{P(A')}\]

📌 Ratio of favourable to unfavourable

🎯 Exam-Ready Insights

Important points to remember — curated from CBSE Board question patterns.

CBSE 4-mark: "Find the probability that a card drawn is a king or a heart" — use addition rule, careful not to double-count the king of hearts.

Sample space construction: list all outcomes systematically (use tree diagrams for multi-step experiments).

Mutually exclusive events cannot happen simultaneously; exhaustive events cover the entire sample space.

P(impossible event) = 0; P(sure event) = 1 — boundary conditions always verified in CBSE.

"At least one" events: P(at least one) = 1 − P(none).

🏆 Competitive Exam Strategy

Targeted tips for JEE Main, JEE Advanced, NEET, BITSAT, and KVPY.

JEE Main

JEE Main probability covers conditional probability P(A|B) and Bayes' theorem (Class XII) — master Chapter 14 deeply as it directly prepares you.

JEE Main

Geometric probability (length or area ratios) appears in JEE — compute the ratio of favourable region to total region.

JEE Advanced

JEE Advanced tests multinomial and combinatorial probability — use combinations from Chapter 6 heavily here.

NEET

Probability in NEET is applied in genetics (Punnett squares represent probability distributions) — understand the biological link.

⚠️ Common Mistakes to Avoid

Not listing the complete sample space — missing outcomes leads to wrong denominators.

Forgetting to subtract P(A∩B) in the addition rule when events are not mutually exclusive.

Confusing "mutually exclusive" with "independent" — these are different concepts.

Writing P(A) > 1 — an immediate red flag that the solution has an error.

💡 Key Takeaways

◆

A sample space S lists ALL possible outcomes of a random experiment.

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Probability is always a number between 0 and 1 (inclusive).

◆

The complement rule is often the quickest path: P(A) = 1 − P(A′).

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The addition theorem avoids double-counting when events can co-occur.

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Probability connects to combinatorics — Chapter 6 (nCr, nPr) is essential prerequisite knowledge.

Probability