Event notation and shaded regions

Which symbol means that both event conditions must hold?

The two only regions stay at 7 and 5, and neither stays at 9. Change how many items are in both. The shaded event is the complement of the overlap

As k changes, what happens to the count outside the overlap?

Read the conditions before counting

Use the universe and both set conditions. A prime complements the whole expression immediately before it

1. 1Intersection Keep items satisfying both conditions \(\displaystyle A\cap B\)
2. 2Union Keep items in at least one set, including the overlap \(\displaystyle A\cup B\)
3. 3Complement A prime means everything in the stated universe outside that set \(\displaystyle A'=S\setminus A\)
4. 4Only and neither A only is in A but outside B. Neither is outside both \(\displaystyle \begin{gathered}A\text{ only}:A\cap B'\\\text{neither}:A'\cap B'\end{gathered}\)
5. 5Counts and probabilities The first line shows three ways to write a count. For uniform selection, divide the event count by the universe count \(\displaystyle \begin{gathered}n(E),\;N(E),\;|E|\\\Pr(E)=\frac{n(E)}{n(S)}\end{gathered}\)
6. 6No common outcomes Mutually exclusive events have an empty intersection. The empty set contains no elements; it is not the number zero \(\displaystyle A\cap B=\varnothing\)

Select the region named by this expression

Select the region named by this expression

Select the region named by this expression

Which expression includes all three regions inside either circle?

How many items belong to this event?

Select one of the 24 items uniformly. Find this probability

Which expression means neither A nor B?

Which regions belong to the complement of the overlap?

The events are mutually exclusive. What is their intersection?

Set

\(\displaystyle \varnothing\)

How many elements are in the empty set?

Which expression means exactly one of A and B?