In this lesson:
By the end of this lesson, you should be able to:
On a card deck, what is "not a heart"?
"Not a heart" can't be just one suit. Hold that thought.
The complement of is everything in that is not in .
"Not A" is all the space outside circle — the rest of the sample space.
"Not A" is every outcome of not in .
Together, and "not A" fill the whole sample space once.
What cards make up "not a heart"?
Commit to your answer, then we'll check it.
Not a heart = all 39 non-heart cards.
The complement is "all the leftovers," not a single other thing.
Write the complement of "a red card" on a 52-card deck.
Pause and answer before the next slide.
Answer: not red = all 26 black cards (clubs and spades).
You now have the full toolkit:
Every everyday description decomposes into these three operations.
"An even number not greater than 4" =
The intersection narrowed it to a single outcome.
"Neither A nor B" means outside both events.
Same set both ways — an equivalence you can see by listing.
Each student is classified by two categories at once.
Pick a random student — an outcome. Any group of cells is an event.
"And" picks one cell; "or" sweeps several — same operations, new grid.
Which single cell is "a tenth-grader who plays a sport"?
Point to it before advancing — it's an intersection.
Answer: the tenth-grade / plays-sport cell (9 students).
Work both yourself. Hint: #1 is an inclusive union; #2 is an intersection with a complement.
Complement trap: "not A" is everything else in , not one other category.
Connective trap: "or" is inclusive union; "and" is intersection, not "combine all."
Spot the connective, map it to its operation.
✓ Not A = the complement = everything else in ✓ Every description decomposes into or, and, not ✓ A two-way table is a sample space
The complement spans all leftovers, not one category
Next: does knowing one event change the chance of another? Independence.
Click to begin the narrated lesson
Describe events as subsets of a sample space