Study Material — 5 PYQs (2018–2020) · Concept Notes · Shortcuts
MNS - Military Nursing Service Probability is a frequently tested subtopic — 5 previous year questions from 2018–2020 papers are included below with concept notes, key rules and shortcut tricks.
MNS - Military Nursing Service Probability — Past Exam Questions
5 questions from actual MNS - Military Nursing Service papers · all shown free · click option to reveal solution
Exam Q 12018Previous Year Pattern
A bag contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is drawn at random from the bag, what is the probability that it is neither red nor green?
Exam Q 22020Previous Year Pattern
A bag contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is drawn at random from the bag, what is the probability that it is neither red nor green?
Exam Q 32020Previous Year Pattern
A bag contains 5 red balls, 7 blue balls, and 8 green balls. Two balls are drawn simultaneously at random from the bag. What is the probability that both balls are of different colours?
Exam Q 42018Previous Year Pattern
A bag contains 4 red balls, 5 blue balls, and 3 green balls. Two balls are drawn at random without replacement. What is the probability that both balls are of the same colour?
Exam Q 52019Previous Year Pattern
A bag contains 5 red balls, 7 blue balls, and 8 green balls. Two balls are drawn simultaneously at random from the bag. What is the probability that both balls are of different colours?
Concept Notes
Probability— Rules & Concept
Core ConceptRead this first — the foundation of the topic
Probability is the mathematical study of uncertainty and chance. It measures how likely an event is to occur. Think of it as a number between 0 and 1, where 0 means impossible and 1 means certain. Core Concept: Probability = Number of favorable outcomes / Total number of possible outcomes. For example, when flipping a coin, probability of heads = 1/2 = 0.5.
Key RulesCore rules you must know cold
Addition Rule
P(A or B) = P(A) + P(B) - P(A and B)
2
Multiplication Rule
P(A and B) = P(A) × P(B) for independent events
3
Complement Rule
P(not A) = 1 - P(A)
4
Conditional Probability
P(A|B) = P(A and B) / P(B)
Formula BlockMemorise — at least one formula appears in every paper
• Basic Probability: P(E) = n(E) / n(S)
• Combination: nCr = n! / (r! × (n-r)!)
• Permutation: nPr = n! / (n-r)!
• Expected Value: E(X) = Σ x × P(x)
Exam PatternsWhat examiners ask — read before attempting PYQs
NDA typically asks card problems, dice problems, bag and ball questions, and conditional probability. Most questions are 2-3 marks. Common formats include: 'What is the probability that...', 'Find the chance of...', 'If two events...'.
ShortcutsUse these to save 30–60 seconds per question
Card Memory Trick
Total cards = 52, Red = 26, Black = 26, Face cards = 12, Aces = 4
2
Dice Sum Shortcut
For two dice, total outcomes = 36. Sum of 7 has maximum probability (6/36 = 1/6)
3. At Least One Formula: P(at least one) = 1 - P(none)
Worked ExampleSolve this step-by-step before moving on
1
Step 1
Total balls = 5 + 3 = 8
2
Step 2
Ways to choose 2 balls from 8 = 8C2 = 28
3
Step 3
Ways to choose 2 red balls from 5 = 5C2 = 10
4
Step 4
Probability = 10/28 = 5/14
Worked Example 2: Two dice are thrown. Find probability that sum is greater than 8.
1
Step 1
Total outcomes = 6 × 6 = 36
2
Step 2
Favorable outcomes (sum > 8): Sum = 9: (3,6), (4,5), (5,4), (6,3) = 4 ways
Sum = 10: (4,6), (5,5), (6,4) = 3 ways
Sum = 11: (5,6), (6,5) = 2 ways
Sum = 12: (6,6) = 1 way
3
Step 3
Total favorable = 4 + 3 + 2 + 1 = 10
4
Step 4
Probability = 10/36 = 5/18
Most
Exam TrapsCommon mistakes students make — avoid these
(#1): Students confuse 'with replacement' and 'without replacement' problems. In without replacement, the sample space changes after each draw. Always check if items are put back or not.
This changes the denominator in subsequent calculations and can completely alter your answer.
Key Points to Remember
Probability always lies between 0 and 1 (inclusive)
A coin is tossed 3 times. What is the probability of getting exactly 2 heads?
Practice 2easy
A bag contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is drawn at random, what is the probability that it is either red or green?
Practice 3easy
A coin is flipped 3 times. What is the probability of getting exactly 2 heads?
Practice 4easy
A bag contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is drawn at random, what is the probability that it is either red or green?
Practice 5medium
A student has a 60% chance of passing Mathematics and a 75% chance of passing English. Assuming independence, what is the probability that the student passes at least one subject?
Practice 6medium
In a lottery, the probability of winning a prize is 0.12. If 500 tickets are sold, how many tickets are expected to win a prize?
Practice 7medium
A box contains 6 defective and 14 non-defective items. If 3 items are drawn at random without replacement, what is the probability that all 3 are non-defective?
Practice 8medium
A bag contains 5 red balls, 7 blue balls, and 8 green balls. If two balls are drawn simultaneously at random, what is the probability that both balls are of the same colour?
Practice 9medium
A bag contains 5 red balls, 7 blue balls, and 8 green balls. If two balls are drawn simultaneously at random, what is the probability that both balls are of the same colour?
Practice 10medium
In a lottery, the probability of winning a prize is 0.15. If 200 tickets are sold and a person buys 8 tickets, what is the probability that this person wins exactly 2 prizes?
Practice 11hard
A bag contains 5 red balls, 7 blue balls, and 8 green balls. Two balls are drawn simultaneously without replacement. What is the probability that both balls are of different colours?
Practice 12hard
A bag contains 5 red balls, 7 blue balls, and 8 green balls. Two balls are drawn simultaneously without replacement. What is the probability that both balls are of different colours?
Practice 13hard
Three fair dice are rolled simultaneously. What is the probability that the sum of the numbers shown is 10, given that at least one die shows a 4?
60-Second Revision — Probability
Remember: Probability = Favorable/Total, always between 0 and 1
Formula: P(at least one) = 1 - P(none) for complex problems
Trap: Check if sampling is with or without replacement
Cards: 52 total, 26 red, 12 face cards, 4 aces per suit
Dice: 36 total outcomes for two dice, sum 7 most probable