1. **Problem Statement:** Define 'Conditional Probability' with a suitable example. 2. **Definition:** Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted as $P(A|B)$, which reads as "the probability of event A given event B." 3. **Formula:** The formula for conditional probability is: $$ P(A|B) = \frac{P(A \cap B)}{P(B)} $$ where: - $P(A \cap B)$ is the probability that both events A and B occur. - $P(B)$ is the probability that event B occurs, and $P(B) > 0$. 4. **Explanation:** This formula tells us how to update the probability of event A when we know event B has happened. We focus only on the outcomes where B occurs and find the fraction of those outcomes where A also occurs. 5. **Example:** Suppose we have a deck of 52 cards. Let event A be "drawing a king" and event B be "drawing a spade." We want to find the probability of drawing a king given that the card drawn is a spade. - Total spades in the deck: 13 - Kings in the deck: 4 - King of spades: 1 Using the formula: $$ P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{1}{52}}{\frac{13}{52}} = \frac{1}{13} $$ So, the probability of drawing a king given that the card is a spade is $\frac{1}{13}$. This example shows how conditional probability narrows down the sample space to the condition event B and then finds the probability of A within that reduced space.