Probability Tests — Pick a Level and Start
Tap a level to see every test in it. Level 1 is set at real SSC CGL difficulty — start there the day you finish the concept. Level 2 is pitched above the exam, to push accuracy under pressure.
Level 1 SSC CGL Level Checking… View tests
Same difficulty as the real SSC CGL paper — one idea applied cleanly. Which numbers can be a probability; the complement rule; one, two, three and four coins; a single die; sums, products, differences and doublets on two dice; three dice; face cards, suits and colours in a pack of 52; cards removed before a draw; draws with replacement; two balls or cards taken together; perfect squares, cubes, primes and factors on numbered tickets; “divisible by a or b” with the overlap removed; coloured balls; finding an unknown count; letters of a word; digits; independent events; truth-tellers; odds; repeated trials; 53 Sundays in a leap year; and committees. A steady score here means the chapter is exam-ready.
Level 2 Above SSC CGL Level Checking… View tests
Harder than the exam asks, because every question chains two ideas or runs one backwards. The number of coins from P(at least one head); a dice total given that a six is showing; a card lost unseen before the draw; the second shooter's accuracy from the chance the target is hit; the second witness's truthfulness from how often they contradict; the original size of a bag after balls are added; “exactly two of three” succeeding; a five-digit number that is a multiple of 4; x from a quadratic inequality; a first success on the third try; odds against “A or B”; and two friends sitting together in a row. Clear these and the real paper feels easy.
Every probability question comes down to one fraction: favourable outcomes ÷ total outcomes, where every outcome in the total is equally likely. The skill is listing the sample space correctly before you count — two dice give 36 ordered pairs, not 21; three coins give 8 outcomes, not 4; and a word with repeated letters has as many outcomes as it has letters, not as many different letters.
The marks are lost in three places. The first is counting an overlap twice — “a king or a spade” is 16 cards, not 17, because the king of spades is both. The second is adding when you should multiply: “A and B” for independent events is a product, and “at least one” is almost always fastest as 1 − P(none). The third is ignoring what the question already tells you — once you know the total on two dice is 8, only the 5 pairs that make 8 are left in play. Each test puts twenty-five probability questions in front of you in one sitting, which is what makes those checks automatic.
How Many Probability Questions Are Asked in SSC CGL?
Probability is a small but steady chapter. It appears now and then in Tier I and a little more regularly in Tier II, and the questions are usually quick marks for anyone who counts the sample space carefully.
| Chapter | Tier I (out of 25) | Tier II Paper I (out of 30) |
|---|---|---|
| Probability (coins, dice, cards, balls, numbers) | 0–1 | 1–2 |
| Statistics (mean, median, mode) | 0–1 | 1–2 |
Counts vary by shift. Probability borrows its counting from number system work — primes, perfect squares and “divisible by a or b” — so those topics make it faster.
What You Will Practice in the Probability Chapter
Basics, coins and dice
- Which values can be a probability, impossible and certain events, and the complement rule
- One, two, three and four coins — exactly, at least and at most a number of heads
- A single die — primes, multiples, factors and the opposite-faces-add-to-7 fact
- Two dice — sums, products, differences, doublets and one number beating the other
- Dice with a given condition, where the known fact shrinks the sample space
- Three dice — all alike, all different and at least one six
Cards, balls, numbers and letters
- A pack of 52 — suits, colours, face cards, number cards and “a king or a spade”
- Cards removed or lost before the draw, and draws with replacement
- Two or three balls or cards taken together, counted with
nCr - Numbered tickets — perfect squares, cubes, primes, factors and “strictly between”
- Divisibility with the overlap removed, over 1 to n and over three-digit numbers
- Coloured balls, finding an unknown count, letters of a word and digits of a number
Independent events, odds and repeated trials
- Both, at least one, exactly one and exactly two of several independent events
- Truth-tellers who agree or contradict each other
- The addition theorem, mutually exclusive events and odds in favour or against
- Repeated trials — exactly k successes, at least one success and the first success on the k-th try
- Leap years and 53 Sundays, and committees chosen from men and women
Rules worth memorising
| Situation | Rule |
|---|---|
| Any event E | P(E) = n(E) / n(S), and 0 ≤ P(E) ≤ 1 |
| Complement | P(not E) = 1 − P(E) |
| At least one | 1 − P(none) |
| A or B | P(A) + P(B) − P(A and B); drop the last term if A and B cannot happen together |
| A and B, independent | P(A) × P(B) |
| n coins | 2n outcomes; exactly r heads in nCr of them |
| Two dice / three dice | 36 / 216 ordered outcomes |
| Divisible by a and b | count the multiples of LCM(a, b), not of a × b |
| Two items taken together | nC2 = n(n − 1)/2 |
| Odds in favour a : b | P = a / (a + b) |
| Two speakers, truth rates p and q | contradict = p(1 − q) + (1 − p)q |
| Exactly r successes in n trials | nCr pr qn−r, with q = 1 − p |
| Leap year | 2 extra days, so P(53 Sundays) = 2/7; an ordinary year gives 1/7 |
The first five rows cover most Tier I questions. The rest are the patterns that turn a long count into one line.
The three mistakes that cost the most marks
- Treating unequal cases as equal. “0, 1 or 2 heads” are not three equally likely cases — one head happens in two ways out of four. Always count from the full list of outcomes.
- Forgetting 1 and 0. 1 is not prime but it is a perfect square and a perfect cube; 0 is a digit. Leaving one of them out, or letting one in, moves the answer to a wrong option.
- Using the old total after a change. When cards are removed or balls are added, both the favourable count and the total change. Recount both before dividing.
Solved Examples — SSC CGL Probability Questions
6 × 6 = 36 ordered outcomes. A total of 9 comes from (3,6), (4,5), (5,4) and (6,3) — 4 outcomes. P = 4/36 = 1/9. Answer: 1/910C2 = 45. Blue pairs: 6C2 = 15. P = 15/45 = 1/3. Multiplying 6/10 × 6/10 would be wrong — that treats the first ball as if it went back. Answer: 1/32/5 × 1/2 = 1/5. P = 1 − 1/5 = 4/5. Answer: 4/5LCM(4, 6) = 12: 5. So 15 + 10 − 5 = 20 and P = 20/60 = 1/3. Answer: 1/3How the Probability Chapter Tests Work
- 25 questions per test, with a full question palette — answered, skipped, marked for review, not visited.
- Every question type in every level — coins, dice, cards, balls, numbers, letters, independent events and odds are spread across the tests so no pattern is missed.
- Optional 15-minute timer — with the clock to build exam speed, without it while you are still learning the chapter.
- Marking: +2 correct, −0.5 wrong, 0 unattempted — the same scheme as the real paper.
- Solutions, shortcut tricks and concept notes open after you submit, question by question.
- English and हिंदी, chosen at the start of every test.
- Free with a TrickySSC account — sign in once with Google or your mobile number, and every test is open to you.
How to Prepare Probability for SSC CGL
- Write the sample space size first. 2, 4, 8 or 16 for coins; 6, 36 or 216 for dice; 52 for cards. Getting the denominator right settles half the question.
- Count ordered pairs on dice. (1, 2) and (2, 1) are different outcomes. A total of 7 happens in 6 ways, not 3.
- Reach for the complement. “At least one”, “neither” and “not” questions are nearly always quicker as
1 −the opposite. - Look for the overlap. Whenever a question says “or”, ask what is counted twice — the king of spades, multiples of the LCM, the number 1.
- Know the pack of 52 by heart. 4 suits of 13; 26 red and 26 black; 12 face cards; 4 aces; 36 number cards from 2 to 10.
- Multiply for “and”, add for “or” — but only for the right events. Multiply when the events are independent; add when they cannot happen together.
- Use what the question tells you. “Given that” or “it is known that” means you count only inside that smaller set.
- Check the answer is between 0 and 1. A total above 1 means something was added twice. One check rules out two options.
- Do Level 1 untimed, the same day you finish the theory. It is set at real SSC CGL difficulty; the aim is counting correctly, not speed.
- Repeat Level 1 with the 15-minute clock on, then move to Level 2. After that, verify against a previous year paper and a full mock test under locked sectional timing.
All SSC CGL Chapter Wise Tests
Every chapter below has its own free Level 1 and Level 2 tests with full solutions.
Browse all 45 chapter tests — Maths (35) · Reasoning (10)
- Number System
- Rule of Divisibility
- Remainder Theorem
- Decimal & Fraction
- LCM & HCF
- Square & Cube Root
- Number Series (AP & GP)
- Power, Indices & Surds
- Algebraic Formula
- Algebraic Result
- Algebraic Expression & Identities
- Percentage
- Profit & Loss
- Discount & Marked Price
- Simple Interest
- Compound Interest
- Ratio & Proportion
- Partnership
- Average
- Problems on Ages
- Mixture & Alligation
- Time & Work
- Pipe and Cistern
- Time, Speed and Distance
- Quadratic Equation
- Boat and Stream
- Races
- Trigonometry
- Heights & Distances
- Geometry
- Mensuration
- Coordinate Geometry
- Probability
- Statistics
- Data Interpretation
- All Maths chapters →
SSC CGL प्रायिकता (Probability) चैप्टर टेस्ट — हिंदी में
प्रायिकता का हर प्रश्न एक ही भिन्न पर टिका है: अनुकूल परिणाम ÷ कुल परिणाम, जहाँ कुल के सभी परिणाम समान रूप से संभावित हों। असली कौशल है गिनने से पहले प्रतिदर्श समष्टि (SAMPLE SPACE) सही लिखना — दो पासों पर 36 क्रमित युग्म होते हैं, 21 नहीं; तीन सिक्कों पर 8 परिणाम, 4 नहीं; और दोहराए अक्षरों वाले शब्द में उतने परिणाम जितने अक्षर हैं।
अंक तीन जगह कटते हैं। पहली: साझा भाग को दो बार गिनना — ‘बादशाह या हुकुम’ 16 पत्ते हैं, 17 नहीं। दूसरी: गुणा की जगह जोड़ देना — स्वतंत्र (INDEPENDENT) घटनाओं में ‘और’ का अर्थ गुणा है, और ‘कम से कम एक’ को 1 − P(एक भी नहीं) से निकालना सबसे तेज़ है। तीसरी: दी गई जानकारी को अनदेखा करना — जब पता हो कि दो पासों का योग 8 है, तो केवल वही 5 युग्म गिने जाते हैं।
TrickySSC पर इस अध्याय के सभी टेस्ट हिंदी में उपलब्ध हैं — प्रश्न, विकल्प, विस्तृत हल और शॉर्टकट ट्रिक सब हिंदी में। दो स्तर हैं: लेवल 1 (SSC CGL के स्तर का) और लेवल 2 (SSC CGL से कठिन)। प्रत्येक टेस्ट में 25 प्रश्न, वैकल्पिक 15 मिनट का टाइमर और +2 / −0.5 की वही मार्किंग जो असली परीक्षा में होती है।