## Questions and Answers

What is the main purpose of providing NCERT Solutions for Class 12 Maths Chapter 13?

What is the focus of Chapter 13 of NCERT Class 12 Maths?

What do students learn in detail in Chapter 13 of Class 12 Maths?

How can the NCERT Solutions for Class 12 Maths Chapter 13 help students?

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In the given scenario, find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.

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Given P(E) = 0.6, P(F) = 0.3, and P(E ∩ F) = 0.2, find P(E|F).

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If a family has two children, what is the conditional probability that both are girls given that the youngest is a girl?

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Compute P(A|B), if P(B) = 0.5 and P(A ∩ B) = 0.32.

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If P(A) = 0.8, P(B) = 0.5, and P(B|A) = 0.4, find P(A ∪ B).

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Evaluate P(A ∪ B), if 2P(A) = P(B) = 5/13 and P(A|B) = 2/5.

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If P(A) = 6/11, P(B) = 5/11, and P(A ∪ B) = 7/11, find P(B|A).

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A fair die is rolled. Find P(E|F), where E = {1,3,5}, F = {2,3}.

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Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

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In a family with two children, what is the conditional probability that at least one is a girl given that at least one is a boy?

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## Study Notes

### Conditional Probability

- The main purpose of providing NCERT Solutions for Class 12 Maths Chapter 13 is to assist students in understanding conditional probability concepts.
- Chapter 13 of NCERT Class 12 Maths focuses on conditional probability, which is a measure of the probability of an event occurring given that another event has occurred.
- In this chapter, students learn in detail about conditional probability, including the concept of conditional probability, properties, and applications.

### Conditional Probability Formulas and Examples

- The conditional probability formula is P(E|F) = P(E ∩ F) / P(F), where E and F are events.
- To find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5, use the formula and plug in the given values.
- If P(E) = 0.6, P(F) = 0.3, and P(E ∩ F) = 0.2, then P(E|F) = P(E ∩ F) / P(F) = 0.2 / 0.3 = 2/3.
- In a family with two children, the conditional probability that both are girls given that the youngest is a girl can be found using the formula.
- Compute P(A|B), if P(B) = 0.5 and P(A ∩ B) = 0.32, using the formula.
- If P(A) = 0.8, P(B) = 0.5, and P(B|A) = 0.4, find P(A ∪ B) using the formula.
- Evaluate P(A ∪ B), if 2P(A) = P(B) = 5/13 and P(A|B) = 2/5.
- If P(A) = 6/11, P(B) = 5/11, and P(A ∪ B) = 7/11, find P(B|A) using the formula.

### More Examples and Applications

- A fair die is rolled, and the conditional probability of event E occurring, given that event F has occurred, can be found using the formula.
- Find P(E|F), where E = {1,3,5}, F = {2,3}.
- The conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4, can be found using the formula.
- In a family with two children, the conditional probability that at least one is a girl given that at least one is a boy can be found using the formula.

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## Description

Access free PDF download of NCERT Solutions for Class 12 Maths Chapter 13 Probability. Understand the concept of probability and the chance of occurrence of an event through detailed explanations and solved examples.