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1.Conditional Probability
Class 12 • Mathematics • NCERT
Conditional Probability
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This lesson explains conditional probability, which deals with the probability of an event occurring given that another event has already occurred, as prescribed in NCERT Class 12.
Lesson Objectives
- Understand the concept of conditional probability.
- Learn the standard NCERT formula.
- Apply conditional probability to problems.
- Prepare for board-exam questions.
1. Meaning of Conditional Probability
Conditional probability is the probability of an event A occurring when another event B has already occurred.
It is denoted by P(A | B).
[ Image Placeholder: Sample Space After Event B ]
2. Definition (NCERT)
If A and B are two events associated with a random experiment and P(B) ≠ 0, then the conditional probability of A given B is defined as:
P(A | B) = P(A ∩ B) / P(B)
[ Image Placeholder: Venn Diagram Showing A ∩ B ]
3. Important Conditions
Certain conditions must be satisfied to apply conditional probability.
• P(B) ≠ 0
• A and B are events of the same experiment
• A and B are events of the same experiment
[ Image Placeholder: Restriction on Sample Space ]
4. Interpretation of Conditional Probability
Conditional probability restricts the sample space to the outcomes where event B has occurred.
Probability is calculated only within the reduced sample space.
[ Image Placeholder: Reduced Sample Space ]
5. NCERT Example
A die is thrown. Let A be the event that the number is even and B be the event that the number is greater than 3.
P(A ∩ B) = 2/6
P(B) = 3/6
P(A | B) = (2/6) ÷ (3/6) = 2/3
[ Image Placeholder: Die Outcomes ]
6. Important NCERT Notes
• Conditional probability depends on occurrence of another event
• P(A | B) ≠ P(A) in general
• Used in probability multiplication theorem
• High-weightage board topic
• P(A | B) ≠ P(A) in general
• Used in probability multiplication theorem
• High-weightage board topic
Practice Questions (NCERT)
- Define conditional probability.
- Write the formula for P(A | B).
- State the condition required to define P(A | B).
- Is P(A | B) always equal to P(A)?
- What does conditional probability depend on?
- Find P(A | B) if P(A ∩ B)=0.2 and P(B)=0.5.
- What happens if P(B)=0?
- Is conditional probability part of NCERT Class 12 syllabus?
- Is it important for board exams?
- Is conditional probability used in Bayes’ theorem?
✅ Show Answer Key
- Probability of A given B
- P(A ∩ B) / P(B)
- P(B) ≠ 0
- No
- Occurrence of B
- 0.4
- Not defined
- Yes
- Yes
- Yes
© Aviate Learning – Conditional Probability (NCERT Class 12)