Probability Theory for SSC CGL Tier 2 Paper 2

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Published on 27 October 2025 by

In SSC CGL Tier 2 SSC JSO (Junior Statistical Officer – Paper II), Probability Theory is an important topic in Statistics & Probability. It helps to quantify uncertainty predicting how likely an event is to occur. Questions are mostly conceptual or formula-based, so a clear understanding is key.

1. What is Probability?

Definition

Probability measures the likelihood of occurrence of an event. It always lies between 0 and 1.

P(E)= Total number of possible outcomes/Number of favourable outcomes​

Event TypeProbability ValueExample
Certain Event1Getting a number ≤ 6 on a die
Impossible Event0Getting number 7 on a die
Likely EventBetween 0 and 1Getting an even number on a die
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2. Key Terms in Probability

Below are the key terms explained:

TermMeaningExample
ExperimentAny activity that produces an outcome.Tossing a coin
Sample Space (S)Set of all possible outcomes.For one coin → {H, T}
Event (E)Subset of sample space.Getting Head = {H}
Mutually Exclusive EventsTwo events cannot occur together.Getting Head and Tail in one toss
Exhaustive EventsAll possible outcomes together.{H, T} for a coin
Independent EventsOccurrence of one does not affect another.Tossing two coins
Dependent EventsOne event affects the probability of another.Drawing cards without replacement
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3. Classical or Theoretical Probability

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4. Complementary Events

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5. Conditional Probability

Definition

Multiplication Theorem of Probability

6. Bayes’ Theorem

Definition

Example of Bayes’ Theorem

7. Properties of Probability

Below are the properties of probability:

PropertyFormula / Explanation
Probability always lies between 0 and 10 ≤ P(E) ≤ 1
Probability of entire sample spaceP(S) = 1
Probability of impossible eventP(Φ) = 0
Addition LawP(A ∪ B) = P(A) + P(B) − P(A ∩ B)
If A and B are mutually exclusiveP(A ∪ B) = P(A) + P(B)

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Key Takeaways for SSC CGL Tier 2 (JSO)

Below are the key takeaways:

  • Probability → measures likelihood of events.
  • Conditional Probability → used when one event depends on another.
  • Bayes’ Theorem → finds probability of a cause given an outcome.
  • Always check whether events are independent or dependent before applying formulas.
  • Common exam focus: conditional probability, Bayes’ theorem, addition & multiplication rules.

FAQs

Q1. What is the range of probability?

Probability always lies between 0 and 1.

Q2. What is conditional probability?

Conditional probability is the probability of an event occurring given that another event has already occurred.

Q3. What is Bayes’ theorem used for?

It helps find the probability of a cause when the effect is known.

Q4. What is the difference between independent and dependent events?

Independent events do not affect each other, while dependent events influence each other’s outcomes.

Q5. Which type of probability questions are most common in SSC CGL Tier 2?

Conditional probability and Bayes’ theorem-based numerical questions are most frequently asked.