प्रायिकता (Probability) – प्रतियोगी परीक्षाओं के लिए BEST शॉर्टकट नियम 2025

प्रायिकता (Probability) – प्रतियोगी परीक्षाओं के लिए शॉर्टकट नियम

Probability is a key topic in the Quantitative Aptitude section of various competitive exams. It helps in measuring the likelihood of an event occurring. Understanding the basic formula, concepts, and tricks can help solve problems faster and more accurately in exams like SSC CGL, RRB NTPC, Bank PO, CDS, and others.

Probability क्या है?

Probability (प्रायिकता) किसी घटना के घटित होने की संभावना को दर्शाती है।

Probability का मूल सूत्र:

इसे दशमलव (0 से 1 के बीच), भिन्न, या प्रतिशत में लिखा जा सकता है।

Important Concepts (महत्वपूर्ण अवधारणाएं):

प्रायिकता (Probability) – प्रतियोगी परीक्षाओं के लिए BEST शॉर्टकट नियम 2025

उदाहरण – Dice, Coin, Cards से जुड़े सवाल:

1️⃣ Coin (सिक्का):

• एक सिक्का उछालने पर – 2 परिणाम: Head (H), Tail (T)
• Probability of Head = 1/2
• Probability of Tail = 1/2

2️⃣ Dice (पासा):

• एक पासे में 1 से 6 तक अंक होते हैं
• Probability of getting even number = 3/6 = 1/2
• Probability of getting a number > 4 = 2/6 = 1/3

3️⃣ Cards:

• एक ताश के पत्तों की गड्डी में कुल 52 पत्ते होते हैं
• Probability of drawing an Ace = 4/52 = 1/13
• Probability of drawing a red card = 26/52 = 1/2

Frequently Asked Formulas

Shortcut Tips:

• “या” (OR) = जोड़
• “और” (AND) = गुणा
• कुल घटनाओं की संख्या = Sample Space
• निश्चित घटना = Probability 1
• असंभव घटना = Probability 0

PROBABILITY PYQS FOR SSC /RAILWAY NTPC 2025

Q1. What is the probability of getting a sum of 9 from two throws of a dice?

Options:
(a) 1/6 (b) 1/8 (c) 1/9 (d) 1/12

Solution : Total outcomes = 6 × 6 = 36

Favorable outcomes (sum = 9):

• (3,6), (4,5), (5,4), (6,3)

→ Total = 4 outcomes

Probability = 4/36 = 1/9

✅ Answer: (c) 1/9

Trick: For dice, always list pairs for required sum.

Q2. A card is drawn from a well-shuffled pack of 52 cards. What is the probability that it is not a face card?

Options:
(a) 10/13 (b) 3/13 (c) 9/13 (d) 11/13

Solution:

Face cards = 3 (J,Q,K) × 4 suits = 12

Not face cards = 52 – 12 = 40

Probability = 40/52 = 10/13

✅ Answer: (a) 10/13

Trick: Face cards = 12; rest = 40.

Q3. A bag contains 5 red and 4 green balls. Two balls are drawn at random. What is the probability that both are red?

Solution :

• Total balls = 5 red + 4 green = 9 balls
• We need to find the probability of choosing 2 red balls from 5 red balls.

Total ways to choose 2 balls out of 9: ⁹ C ₂ = 36

Favorable ways to choose 2 red balls out of 5 : ⁵ C ₂ = 10

Probability = fav. event / total fav. event = 10/36

= 5/18 Ans.

Q4. A card is drawn from a pack of 52 cards. What is the probability of drawing a king or a queen?

Options:
(a) 1/13 (b) 2/13 (c) 3/13 (d) 1/26

Solution:

Kings = 4, Queens = 4 ⇒ Total = 8

P = 8/52 = 2/13

✅ Answer: (b) 2/13

Trick: 4 kings + 4 queens

Q5.What is the probability that a leap year selected at random will contain 53 Sundays?

Options:
(a) 1/7 (b) 2/7 (c) 3/7 (d) 4/7

Solution:

A leap year has 366 days = 52 weeks + 2 days
→ Extra days: (Sunday, Monday), (Monday, Tuesday), …, (Saturday, Sunday) → 7 combinations

Favorable: (Sunday, Monday), (Saturday, Sunday) = 2

P = 2/7

✅ Answer: (b) 2/7

Trick: Extra 2 days in leap year = 2/7 cases with 53 Sundays

Quick Tricks Recap for SSC CGL/ NTPC RAILWAY :

Scenario	Trick
Coin toss	2 outcomes: H, T
One die	6 outcomes
Two dice	36 outcomes
Card deck	52 total, 13 per suit, 12 face cards
Drawing without replacement	Use combinations
Leap year extra days	Look at extra 1 or 2 days (365 or 366 days)