Probability (प्रायिकता) – NDA Preparation

Goal of this chapter: By the end of this lesson, you will feel confident with the key NDA-level concepts of Probability (प्रायिकता) and be able to solve exam-style questions on your own.

हिंदी Note: इस chapter को आराम से पढ़िए – examples और छोटे-छोटे अभ्यास के साथ। एक बार समझ आ गया तो NDA में Probability (प्रायिकता) के सवाल आपके लिए बहुत आसान हो जाएंगे 😄

📘 Introduction (परिचय)

Probability is the branch of mathematics that deals with the likelihood of events occurring. It helps us quantify uncertainty in daily life or experiments.

प्रायिकता गणित की वह शाखा है जो किसी घटना के घटित होने की संभावना का अध्ययन करती है।

📌 Important Formulas & Tips (महत्वपूर्ण सूत्र और टिप्स)

1. Probability of an event = (Favorable outcomes) / (Total outcomes)

2. 0 ≤ Probability ≤ 1

3. Probability of not happening = 1 - Probability of happening

4. For mutually exclusive events A and B: P(A or B) = P(A) + P(B)

5. For independent events A and B: P(A and B) = P(A) × P(B)

🧠 NDA Practice Questions with Hints (संकल्पनात्मक प्रश्न)

Q1. A coin is tossed once. What is the probability of getting a tail?
Hint: Total outcomes = 2 (Head, Tail)
Answer: 1/2

Q2. A dice is rolled. What is the probability of getting an even number?
Hint: Even numbers are 2, 4, 6
Answer: 3/6 = 1/2

Q3. From a deck of 52 cards, what is the probability of drawing a queen?
Hint: There are 4 queens in a deck
Answer: 4/52 = 1/13

Q4. What is the probability of drawing a red card from a deck?
Hint: 26 red cards (13 hearts + 13 diamonds)
Answer: 26/52 = 1/2

Q5. A number is chosen from 1 to 5. What is the probability of choosing 4?
Hint: Total = 5 numbers, Favorable = 1
Answer: 1/5

📝 Additional Practice Questions (उत्तर सहित अभ्यास)

Q1. What is the probability of getting a 5 when a dice is thrown? – 1/6
Q2. In a family of 3 children, what is the probability that there are 2 boys and 1 girl? – 3/8
Q3. A letter is chosen from the word ‘PROBABILITY’. What is the probability of selecting a vowel? – 4/11
Q4. Probability of getting head in 3 coin tosses? – 1/8 for 3 heads
Q5. What is the probability of drawing a spade from a deck? – 13/52 = 1/4

Ask Doubt

Quick Recap | सार

Now you should be able to:

Recall the key ideas of this chapter without looking at the book.
Solve most NDA-style questions of this topic step by step.
Identify and avoid the most common traps used in competitive exams.

Self-check: अगर practice questions अपने आप हो रहे हैं, तो chapter strong है। जो सवाल अटकते हैं, बस उन्हें दोबारा देख लें।

Common Exam Mistakes | आम गलतियाँ

जल्दी-जल्दी में question पूरा पढ़े बिना solve करना।
Sign (+/−) या power गलत लिख देना।
Last step में calculation check न करना – आधा काम सही, answer गलत।

ध्यान रखिए: NDA में topper वो नहीं जो सब कुछ जानता है, बल्कि वो है जो छोटी-छोटी गलतियाँ avoid कर देता है।