Please could someone explain what P(A $\cup$ B) means? and how you know what its out of?

Question

In statistics I can understand every other thing but this! Someone please help!

Answer 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 $6$.

Answer 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

Answer 3

Suppose that there are $n$ events possible. Let $A$ be a set of $n - k$ arbitrary events and $B$ the set of other $k$ events. Then $\rm A \cup B$ denotes all the events possible.

$P({\rm A \cup B})$ denotes the probability of an event happening from either of set $\rm A$, or $\rm{B}$ (which would be $1$ in this case since all events possible are contained within $\rm A \cup B$).

Example. Suppose we are throwing a fair dice. Let $\rm O$ denote the set of events where the number we get is odd. Let $\rm E$ denote the set of events where the number we get is even. It is obvious that,$$\begin{aligned} \rm O &= \{1,3,5\} \\ \rm E &= \{2,4,6\} \\\rm O \cup E & = \{1,2,3,4,5,6\} \end{aligned}$$

Property. If $\rm A \cap B = \emptyset$, then $\rm P(A \cup B) = 1$ (if $A$ and $B$ are the only sets).

Pop Quiz.

• What do you infer from $\rm P(A \cap B)$?
• Can you find other properties for different cases?