Understanding Conditional Probability with an Example

# Understanding Conditional Probability with an Example Video Lecture | Mathematics (Maths) Class 12 - JEE

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

## FAQs on Understanding Conditional Probability with an Example Video Lecture - Mathematics (Maths) Class 12 - JEE

 1. What is conditional probability?
Ans. Conditional probability is a mathematical concept that measures the likelihood of an event occurring given that another event has already occurred. It is denoted by P(A|B), where A and B are two events. It helps us understand the relationship between two events and how the occurrence of one event influences the probability of the other.
 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) represents the probability of both events A and B occurring simultaneously, and P(B) represents the probability of event B occurring. By dividing the probability of both events occurring by the probability of event B, we obtain the conditional probability of event A given event B.
 3. Can you give an example of conditional probability?
Ans. Sure! Let's consider an example: Suppose we have a deck of cards and we draw two cards successively without replacement. What is the probability of drawing a king on the second draw, given that the first card drawn was a king? Here, the probability of drawing a king on the first draw is 4/52 (since there are 4 kings in a deck of 52 cards). After the first king is drawn, there are now 51 cards remaining, with 3 kings left. Therefore, the probability of drawing a king on the second draw, given that the first card drawn was a king, is 3/51.
 4. How is conditional probability related to independent events?
Ans. If two events, A and B, are independent, then the occurrence of one event does not affect the probability of the other event. In this case, the conditional probability is simply the probability of event A, as it is not influenced by event B. Mathematically, if A and B are independent, then P(A|B) = P(A).
 5. Can conditional probability be greater than 1?
Ans. No, conditional probability cannot be greater than 1. The probability of an event occurring is always between 0 and 1, inclusive. If the conditional probability of event A given event B is greater than 1, it implies that the probability of event A occurring is greater than the probability of event B occurring, which is not possible.

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

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