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SSC MTS Probability

Study Material — 3 PYQs (2021–2021) · Concept Notes · Shortcuts

SSC MTS Probability is a frequently tested subtopic — 3 previous year questions from 2021–2021 papers are included below with concept notes, key rules and shortcut tricks.

3 PYQs

2021–2021

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Previous Year Questions

SSC MTS Probability — Past Exam Questions

3 questions from actual SSC MTS papers · all shown free · click option to reveal solution

Exam Q 12021Previous Year Pattern

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?

Exam Q 22021Previous Year Pattern

A student has a 70% chance of passing Mathematics and a 60% chance of passing English. Assuming independence, what is the probability that the student passes at least one subject?

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Exam Q 32021Previous Year Pattern

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?

Concept Notes

Probability— Rules & Concept

💡

Core Concept

Read this first — the foundation of the topic

→Core Concept

Probability = Favorable Outcomes / Total Possible Outcomes. The value always lies between 0 and 1. If probability is 0, the event will never happen. If it's 1, the event will definitely happen

🔑Addition Rule

For mutually exclusive events A and B, P(A or B) = P(A) + P(B) 2

💡Multiplication Rule

For independent events A and B, P(A and B) = P(A) × P(B) 3

→Complementary Events

P(A) + P(not A) = 1, so P(not A) = 1 - P(A) 4

→Conditional Probability

P(A given B) = P(A and B) / P(B)

🔢

Formula Block

Memorise — at least one formula appears in every paper

• Basic Probability = Favorable outcomes / Total outcomes

• Probability of at least one = 1 - Probability of none

• Odds in favor = Favorable : Unfavorable

• Expected value = Sum of (Probability × Value)

📊

Exam Patterns

What examiners ask — read before attempting PYQs

✏️Worked Example 1

1

Count total balls = 5 + 3 + 2 = 10

2

Count favorable outcomes (red balls) = 5

3

Apply formula = 5/10 = 1/2 = 0.5 Answer: 1/2 or 50% Shortcut Trick #2 - Card Problems Quick Reference: Remember that a deck has 52 cards with 13 cards of each suit (hearts, diamonds, clubs, spades). Face cards are 12 in total (4 each of Jack, Queen, King)

✏️Worked Example 2

1

Total possible outcomes when throwing two dice = 6 × 6 = 36

2

Find favorable outcomes for sum = 7 (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 outcomes

3

Apply formula = 6/36 = 1/6 Answer: 1/6 Shortcut Trick #3 - Dice Sum Patterns: For two dice, sum of 7 has maximum probability (6/36), while sums of 2 and 12 have minimum probability (1/36 each). Common Mistake #1: Students often forget to consider all possible arrangements. For example, when drawing 2 balls from a bag, they count (Red, Blue) but forget (Blue, Red) as a separate case when order matters. Always check whether the problem requires considering order or not. Another frequent error is mixing up 'with replacement' and 'without replacement' scenarios. In 'with replacement', the total number of items remains the same for each draw. In 'without replacement', the total decreases after each draw, affecting subsequent probabilities.

Key Points to Remember

Probability always lies between 0 and 1 inclusive
Basic formula: Probability = Favorable outcomes / Total outcomes
For 'at least one' problems, use complement: P(at least one) = 1 - P(none)
Standard deck has 52 cards, 13 per suit, 12 face cards total
Two dice have 36 total outcomes, sum of 7 has highest probability
Mutually exclusive events: P(A or B) = P(A) + P(B)
Independent events: P(A and B) = P(A) × P(B)
Complementary events: P(A) + P(not A) = 1
Always check if order matters in the problem statement
With replacement vs without replacement changes denominators

Exam-Specific Tips

A standard deck contains exactly 52 cards with 4 suits of 13 cards each
Number of face cards in a deck is 12 (4 Jacks, 4 Queens, 4 Kings)
Two dice thrown together give 36 total possible outcomes
Sum of 7 with two dice can occur in exactly 6 ways
Probability of getting heads in a fair coin toss is exactly 1/2
In a standard deck, probability of drawing an ace is 4/52 = 1/13
Maximum probability value is 1, minimum probability value is 0
Number of ways to arrange n distinct objects is n! factorial

60-Second Revision — Probability

Formula: Probability = Favorable outcomes / Total outcomes
Remember: Use 1 - P(none) for 'at least one' questions
Trap: Don't confuse with replacement and without replacement scenarios
Quick fact: Standard deck = 52 cards, Face cards = 12
Pattern: Two dice sum of 7 has maximum probability of 1/6
Rule: Always check if order matters in arrangement problems
Shortcut: P(not A) = 1 - P(A) for complement problems

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