Compound Probability Example

Let’s illustrate compound probability with an example:

Example: Suppose a bag contains 5 red marbles and 3 blue marbles. If two marbles are randomly selected from the bag without replacement, what is the probability of selecting one red marble and one blue marble?

Solution:

Selecting a Red Marble:

Probability of selecting the first red marble = 5/8

After selecting the first red marble, there are 4 red marbles left and a total of 7 marbles remaining.

Probability of selecting the second red marble = 4/7

Probability of selecting one red marble = (5/8) × (4/7) = 5/14

Selecting a Blue Marble:

Probability of selecting the first blue marble = 3/8

After selecting the first blue marble, there are 3 blue marbles left and a total of 7 marbles remaining.

Probability of selecting the second blue marble = 3/7

Probability of selecting one blue marble = (3/8) × (3/7)

= 9/56

Compound Probability:

Probability of selecting one red and one blue marble = Probability of selecting a red marble * Probability of selecting a blue marble

Probability = (5/14) × (9/56)

= 45/784

Compound probability is a fundamental concept in mathematics and statistics that deals with the likelihood of multiple events occurring together within a single experiment or scenario. It provides a framework for understanding the combined probability of two or more events happening simultaneously or sequentially. Compound probability plays a crucial role in various fields such as statistics, finance, and engineering, where events often depend on the occurrence of other events.