Class 10 Maths — Chapter 14: Probability

By RAAM SETU | NEET, SSC, Railway & Police Bharti Focused Notes 📘

📘 Introduction

This chapter covers Probability — a measure of how likely events are to occur. Learn random experiments, outcomes, events, favorable outcomes, and probability formulas. Essential for NEET, SSC, Railway, Police Bharti and Class 10 board exams.

🔹 Key Formulas

📊 Chapter Summary Table

Concept Formula / Definition Use
Probability of EP(E) = favorable / totalMeasures chance of event
Complementary EventP(E') = 1 − P(E)Used in calculations
Sum RuleΣP(E) = 1Total probability check

🧮 Practice Questions

  1. A die is rolled. Find probability of getting a 4.
  2. A coin is tossed twice. Probability of getting exactly one head?
  3. A bag contains 5 red and 3 green balls. Probability of picking a red ball?
  4. Find probability of an impossible event.
  5. Calculate the probability of getting a number greater than 3 on a die.

Probability — Class 10 (Concise & Exam-ready)

Sample space • Events • Classical probability • Complementary events • Mutually exclusive • Basic conditional ideas • Practice
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1. Basic Definitions

Experiment: Any process that yields results (e.g., toss a coin).

Sample space (S): Set of all possible outcomes. Example: for a die S = {1,2,3,4,5,6}.

Event: Any subset of the sample space (e.g., rolling an even number {2,4,6}).

2. Classical (Simple) Probability

When all outcomes are equally likely:

P(E) = (Number of favourable outcomes) / (Total number of outcomes) = |E| / |S|

Probability values range from 0 to 1. P(E)=0 impossible, P(E)=1 certain.

3. Basic Rules of Probability

  • Complement rule: P(E') = 1 − P(E) where E' is complement of E.
  • Addition rule (for any two events): P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
  • For mutually exclusive events (disjoint): P(A ∪ B) = P(A) + P(B) because P(A ∩ B) = 0.
  • Probability bounds: 0 ≤ P(E) ≤ 1.

4. Types of Events — Quick

  • Simple event: consists of a single outcome.
  • Compound event: consists of more than one outcome (e.g., even or multiple of 3).
  • Complementary event: E' contains all outcomes not in E.
  • Mutually exclusive: events that cannot happen together.
  • Exhaustive: collection of events whose union is the sample space.

5. Intro to Conditional Probability (Simple idea)

Conditional probability P(A|B) is probability of A given that B has occurred. For class 10 we introduce basic conceptual idea and simple computation when needed:

P(A|B) = P(A ∩ B) / P(B) , provided P(B) > 0.

Example idea: drawing two cards without replacement — probability of second being an ace given first was an ace.

6. Solved Examples

Example 1. A fair die is rolled. Find probability of getting an even number.

Favourable outcomes = {2,4,6} ⇒ 3 outcomes. Total = 6 ⇒ P = 3/6 = 1/2.

Example 2. From a pack of 52 cards, find P(heart) = 13/52 = 1/4.

Example 3 (Complement rule). Probability that in one toss of a fair coin you do not get head = 1 − 1/2 = 1/2.

Example 4 (Mutually exclusive). If two dice are rolled, find P(sum = 2 or sum = 3). P(sum=2)=1/36, P(sum=3)=2/36 ⇒ since disjoint, P=3/36=1/12.

Example 5 (Conditional idea). Two cards drawn without replacement. Probability both are aces = (4/52)×(3/51) = 1/221. Then P(second ace | first ace) = 3/51 = 1/17.

7. Practice Questions

  1. A bag contains 5 red and 3 blue balls. One ball is picked at random. Find probability it is red.
  2. A coin is tossed three times. Find probability of getting exactly two heads.
  3. From a deck, two cards are drawn without replacement. Find probability both are kings.
  4. Die is rolled. Find probability of getting a number greater than 4 or an even number (use addition rule).

8. Exam Tips & Quick Strategies

  • Carefully list sample space for small experiments (coin, die, two cards) to avoid missing outcomes.
  • Use complement rule when "at least one" phrasing appears — often easier: P(at least one) = 1 − P(none).
  • For multiple-step draws, pay attention to replacement vs no replacement — it changes probabilities.
  • Label favourable outcomes explicitly to avoid mental slips when counting.