Conditional Probability

Conditional probability is the probability of an event happening given that another event has already occurred. It is denoted by P(A|B), which represents the probability of event A occurring given that event B has already occurred.

Calculating Conditional Probability

The formula to calculate conditional probability is:

P(A|B) = P(A and B) / P(B)

Where:

• P(A|B) = conditional probability of A given B
• P(A and B) = probability of both A and B occurring
• P(B) = probability of event B occurring

Example

Suppose we have a deck of playing cards. What is the probability of drawing a king from a deck of cards given that the card drawn is a spade?

Let's calculate this using conditional probability:

P(King|Spade) = P(King and Spade) / P(Spade)

There are 13 spades in a deck of 52 cards, so P(Spade) = 13/52 = 1/4

There are 4 kings in a deck of 52 cards, so P(King and Spade) = 1/52

Therefore, P(King|Spade) = (1/52) / (1/4) = 1/13

Study Guide

Here are some key points to remember about conditional probability:

1. Conditional probability is the probability of an event occurring given that another event has already occurred.
2. It is calculated using the formula P(A|B) = P(A and B) / P(B).
3. When calculating conditional probability, always make sure to consider the probability of the given condition occurring.
4. Conditional probability is used in various real-life scenarios, such as medical diagnoses, weather forecasting, and risk assessment.

Practice calculating conditional probability with different examples to strengthen your understanding of the concept.

[Conditional Probability] Related Worksheets and Study Guides:

• ProbabilityMathematics • Fourth Grade