Conditional Probability

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

Formula for Conditional Probability

The formula for conditional probability is:

P(A|B) = P(A ∩ B) / P(B)

Where P(A ∩ B) is the probability of both event A and event B occurring, and P(B) is the probability of event B occurring.

Example

Let's consider an example to understand conditional probability better. Suppose we have a bag containing 3 red balls and 2 green balls. If we draw a ball from the bag without replacement, what is the probability of drawing a green ball given that the first ball drawn was red?

We can use the formula for conditional probability to solve this:

P(Green|Red) = P(Green ∩ Red) / P(Red)

Since we are drawing without replacement, the probability of drawing a green ball after drawing a red ball is:

P(Green ∩ Red) = (2/4) * (3/5) = 6/20

P(Red) = 3/5

Therefore, the conditional probability of drawing a green ball given that the first ball drawn was red is:

P(Green|Red) = (6/20) / (3/5) = 6/12 = 1/2

Study Guide

Here are some key points to remember when studying conditional probability:

Understand the concept of conditional probability as the likelihood of an event occurring given that another event has already occurred.
Learn the formula for conditional probability: P(A|B) = P(A ∩ B) / P(B)
Practice solving problems involving conditional probability, especially those that involve drawing without replacement or other dependent events.
Understand how to interpret the results of conditional probability in real-world scenarios.

By mastering conditional probability, you will be able to analyze and understand the likelihood of events occurring in various situations, making it a valuable skill in many fields, including mathematics, statistics, and decision-making.

◂Math Worksheets and Study Guides Fourth Grade. Probability

The resources above cover the following skills:

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

Data Analysis and Probability (NCTM)

Understand and apply basic concepts of probability.

Describe events as likely or unlikely and discuss the degree of likelihood using such words as certain, equally likely, and impossible.

Understand that the measure of the likelihood of an event can be represented by a number from 0 to 1.

Connections to the Grade 4 Focal Points (NCTM)

Number and Operations: Building on their work in grade 3, students extend their understanding of place value and ways of representing numbers to 100,000 in various contexts. They use estimation in determining the relative sizes of amounts or distances. Students develop understandings of strategies for multi-digit division by using models that represent division as the inverse of multiplication, as partitioning, or as successive subtraction. By working with decimals, students extend their ability to recognize equivalent fractions. Students' earlier work in grade 3 with models of fractions and multiplication and division facts supports their understanding of techniques for generating equivalent fractions and simplifying fractions.

Conditional Probability

Formula for Conditional Probability

Example

Study Guide

[Conditional Probability] Related Worksheets and Study Guides:

◂Math Worksheets and Study Guides Fourth Grade. Probability

The resources above cover the following skills: