How to Find Probability of a Compound Event
Concept
The probability of an event is the measure of the possibility of the occurrence of that event. Compound probability is applicable when there are more than one independent events happening. Suppose, you need to roll a die, and toss a coin; this is an example of a compound event.
Rules
To find the probability of two dependent events:
1. Find the probability of each event. Remember to subtract 1 from the total number of events for the second event.
2. Multiply the probability of the events
To find the probability of independent events:
1. Find the probability of each event
2. Find the product of the individual probabilities.
Example
If a boy picks a cube from each container, what is the probability of picking a red from the first container and a yellow from the second container?
Solution
1. Find the probability of the first event.
There is 1 red cube and a total of 6 cubes in the first container. The probability of getting a red cube is .
2. Find the probability of the second event.
There are 3 yellow cubes in the second container. There are a total of 5 cubes in the container. The probability of getting a yellow cube is .
3. These are independent events. What occurs in the first container does not affect what occurs in the second container. To find the probability of both events happening, multiply the probability of the first event by the probability of the second event.
This can be reduced to
Practice How to Find Probability of a Compound Event
Practice Problem 1
What is the probability of rolling a 6 and landing on blue?
Practice Problem 2
What is the probability of getting red on the first spinner and yellow on the second spinner?
Practice Problem 3
If a boy picks a cube from each container, what is the probability of picking a blue cube from the first container and a yellow cube from the second container?
Practice Problem 4
What is the probability of flipping 3 tails in a row?
Write your answer as a fraction.
Probability is the likelihood that an event will occur. It is written as a fraction with the number of favorable outcomes as the numerator and the total number of outcomes as the denominator.
A compound event is one in which there is more than one possible outcome.
Dependent events: The outcome of one event changes the outcome of another event.
Independent events: The outcome of one event does not change the outcome of another event.