3 questions from actual SSC MTS papers · all shown free · click option to reveal solution
Probability is the mathematical way to measure how likely an event is to happen. Think of it as a fraction that tells you the chances of something occurring. In SSC CGL, probability questions appear in almost every paper and can fetch you easy marks if you master the basic concepts and shortcuts. 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.
For mutually exclusive events A and B, P(A or B) = P(A) + P(B) 2
For independent events A and B, P(A and B) = P(A) × P(B) 3
P(A) + P(not A) = 1, so P(not A) = 1 - P(A) 4
P(A given B) = P(A and B) / P(B)
SSC CGL typically asks about card problems, dice problems, ball drawing from bags, and coin tossing. Questions often involve finding probability of getting specific combinations or calculating odds.
#1 - For 'At Least One' Problems: Instead of calculating all possible combinations, use the complement rule. Find the probability that the event doesn't happen at all, then subtract from 1.
Count total balls = 5 + 3 + 2 = 10
Count favorable outcomes (red balls) = 5
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: Two dice are thrown. What is the probability of getting a sum of 7?
Total possible outcomes when throwing two dice = 6 × 6 = 36
Find favorable outcomes for sum = 7 (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 outcomes
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).
#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.