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Conditional Probability : Properties Video Lecture | Mathematics (Maths) for JEE Main & Advanced

Q: 3. What are the properties of conditional probability?

Ans. The properties of conditional probability include:- The probability of an event A given event B is always between 0 and 1.- If two events A and B are independent, then the conditional probability of A given B is equal to the probability of A, i.e., P(A|B) = P(A).- If two events A and B are mutually exclusive, then the conditional probability of A given B is 0, i.e., P(A|B) = 0.- The conditional probability of the complement of an event A, given event B, is equal to 1 minus the conditional probability of A given B, i.e., P(A'|B) = 1 - P(A|B).

FAQs on Conditional Probability : Properties Video Lecture - Mathematics (Maths) for JEE Main & Advanced

1. What is conditional probability?

Ans. Conditional probability is a measure of the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), where A and B are two events. It represents the probability of event A happening, given that event B has already occurred.

2. How is conditional probability calculated?

Ans. Conditional probability is calculated using the formula: P(A|B) = P(A ∩ B) / P(B), where P(A ∩ B) is the probability of both events A and B occurring together, and P(B) is the probability of event B happening.

3. What are the properties of conditional probability?

Ans. The properties of conditional probability include: - The probability of an event A given event B is always between 0 and 1. - If two events A and B are independent, then the conditional probability of A given B is equal to the probability of A, i.e., P(A|B) = P(A). - If two events A and B are mutually exclusive, then the conditional probability of A given B is 0, i.e., P(A|B) = 0. - The conditional probability of the complement of an event A, given event B, is equal to 1 minus the conditional probability of A given B, i.e., P(A'|B) = 1 - P(A|B).

4. How is conditional probability useful in real-life scenarios?

Ans. Conditional probability is widely used in various real-life scenarios, including: - Medical diagnosis: It helps in determining the probability of a certain disease given the symptoms exhibited by a patient. - Weather forecasting: It helps in predicting the probability of rain based on the current weather conditions. - Risk assessment: It helps in evaluating the probability of certain risks occurring based on various factors. - Market analysis: It helps in determining the probability of a product being purchased based on customer demographics and behavior. - Fraud detection: It helps in identifying suspicious activities based on patterns and conditional probabilities.

5. What is the difference between conditional probability and joint probability?

Ans. Conditional probability focuses on the probability of an event occurring given that another event has already occurred. On the other hand, joint probability focuses on the probability of two or more events occurring together. Conditional probability is calculated based on the joint probability and the probability of the conditioning event.

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Sep 08, 2025 Last updated

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	Mathematics (Maths) for JEE Main & Advanced 176 videos\|582 docs\|160 tests

Mathematics (Maths) for JEE Main & Advanced

176 videos|582 docs|160 tests

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