How to Find the Probability of Compound Event?
Compound probability is the probability of two or more independent events occurring together. In this article, you will learn how to find the probability of a compound event in a few simple steps.
Find the Probability of Compound Event: what to notice and how to work it
What to notice first
Common student mistake
Key formulas and cues
A reliable path
- List outcomesName the possible results or count them carefully.
- Choose the ruleUse addition, multiplication, or conditional probability based on the wording.
- Check the rangeA probability must be between 0 and 1.
Worked examples
Simple probability
- Even outcomes are 2, 4, and 6.
- There are 3 favorable outcomes out of 6.
- Reduce the fraction.
Independent events
- P(heads) = 1/2 for each flip.
- The flips are independent.
- Multiply 1/2 by 1/2.
Try one before moving on
Find the Probability of Compound Event: pop-up practice
Related Topics
A step-by-step guide to finding the probability of a compound event
The compound probability of compound events (mutually inclusive or mutually exclusive) can be defined as the probability of two or more independent events occurring together. An independent event is an event whose outcome is not affected by the outcomes of other events.
Type the problems from this lesson and check each step.
A mutually inclusive event involves a situation where one event cannot occur with the other while an exclusive mutual event is when both events cannot occur at the same time. The compound probability will always lie between \(0\) and \(1\).
Compound probability formulas
There are two formulas for calculating compound probability depending on the type of events that occur.In general, to find the compound probability, the probability of the first event is multiplied by the probability of the second event, and so on. The compound probability formulas are given below:
Mutually exclusive events compound the probability
\(\color{blue}{P(A\: or B) = P(A) + P(B)}\)
Using set theory, this formula is presented as follows:
\(\color{blue}{P\left(A\:∪\:B\right)\:=\:P\left(A\right)\:+\:P\left(B\right)}\)
Mutually inclusive events compound the probability
\(\color{blue}{P\left(A\:or\:B\right)\:=\:P\left(A\right)\:+\:P\left(B\right)\:-\:P\left(A\:and\:B\right)}\)
\(\color{blue}{P\left(A\:∪\:B\right)\:=\:P\left(A\right)\:+\:P\left(B\right)\:-\:P\left(A\:⋂\:B\right)}\)
where \(A\) and \(B\) are two independent events, and \(\color{blue}{P\left(A\:and\:B\right)\:=\:P\left(A\right)\times \:P\left(B\right)}\)
Finding the Probability of Compound Event, Example 1:
If a dice is rolled, find the compound probability that either a \(2\) or \(4\) will be obtained.
Solution: \(P (2)=\frac {1}{6}\), \(P(4)= \frac{1}{6}\)
Since this is an example of a mutually exclusive event, therefore, the compound probability formula is used: \(P\left(A\:or\:B\right)\:=\:P\left(A\right)\:+\:P\left(B\right)\)
\(P (2\: or\: 3)=\frac {1}{6}+\frac {1}{6}\)
\(=\frac {1}{3}\)
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