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 $B$).

see http://en.wikipedia.org/wiki/Probability#Mathematical_treatment

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Jamie Hawk
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Updated on June 13, 2022

Comments

  • Jamie Hawk
    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
      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
      Clumsy cat about 5 years
      Is this downvoted because it rudimentary?
    • John Doe
      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
    Elements in Space over 9 years
    is there something wrong with my eyes or does B appear larger than A for some reason?