# What is the meaning of \$P(A \cup B)\$ in probability and statistics?

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## Solution 1

\$P(A\cup B)\$ is simply the probability that at least one of \$A\$ and \$B\$ occurs. \$\cup\$ is the symbol for set union, and events in probability theory are described by sets.

For example, take throwing a die. Take \$A\$ to be the event "an even number was thrown", represented by the set \$\{2,4,6\}\$ and \$B\$ to be the event "a prime number was thrown", represented by the set \$\{2,3,5\}\$. Then \$A\cup B\$ is the event "an even number or a prime number was thrown", that is, the union \$A\cup B=\{2,3,4,5,6\}\$.

Then \$P(A\cup B)\$ is the probability that you've thrown an even or a prime number, that is the probability that your result was one of the numbers from \$2\$ to \$6\$.

## Solution 2

If \$A,B\$ are two events ,then,

\$P(A\cup B) \$ represents the probability of happening atleast one of the event(\$A\$ or \$B\$).

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### Jamie Hawk

Updated on June 13, 2022

• Jamie Hawk about 19 hours

In probability, letters \$A\$ and \$B\$ are used to denote various events. Then we write \$P(A)\$ for the probability of event \$A\$ happening. Same for \$P(B)\$.

But I often see the notation \$P(A\cup B)\$ as well. What does it mean, and how is such a thing calculated?

• Neal over 9 years
Do you remember studying sets? This is the probability of the event \$A\cup B\$, the union of events \$A\$ and \$B\$. It represents the probability of \$A\$ or \$B\$.
• Clumsy cat about 5 years
Is this downvoted because it rudimentary?
• John Doe over 4 years
@TheoreticalPerson the original version of the question was quite bad, it has been improved since (see the editing history)
• Elements in Space over 9 years
is there something wrong with my eyes or does B appear larger than A for some reason?