Precalculus uses the addition rule with counting: each event is counted with combinations, and the counts are added when the events cannot happen together. Questions about committees, hands of cards and arrangements are the usual setting.
Also taught in Algebra 2 and Statistics, each at its own level and with its own examples.
The preview can look cramped on a phone. The PDF and printed sheet come out normal.
3 people are chosen from 5 boys and 4 girls. Find P(all boys or all girls)
Total groups: C(9, 3) = 84.
All boys: C(5, 3) = 10. All girls: C(4, 3) = 4.
A group cannot be both, so add: (10 + 4)/84.
The answer is 61.
Where students go wrong
Adding events that overlap. All boys and at least two boys can describe the same group, so check whether one outcome fits both before you skip the subtraction.
Also called probability of A or B, addition rule or overlapping events.
What you can put on this worksheet
One event or the other
A 6-sided die is rolled. Find P(greater than 3 or less than 3).→ 65
Mutually exclusive or not?
A die is rolled. Are rolling a number less than 3 and rolling a prime number mutually exclusive?→ No
Overlapping events
One card is drawn from a standard deck. Find P(a black card or a king).→ 137
Or, when each item has a color and a number
A box has 9 dark chocolates, 1 of them with nuts, and 10 milk chocolates, 5 of them with nuts. One is picked at random. Find P(milk or with nuts).→ 1911
Mutually exclusive? From the numbers
P(A)=0.4, P(B)=0.4, and P(Aand B)=0.05. Are A and B mutually exclusive?→ No: P(Aand B)=0
Find the missing probability with the addition rule
A and B are mutually exclusive. P(A)=0.4and P(Aor B)=0.8. Find P(B)→ 0.4
Questions about these worksheets
Yes. Every mutually exclusive events sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the mutually exclusive events questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 6: one event or the other, mutually exclusive or not?, overlapping events, or, when each item has a color and a number, mutually exclusive? from the numbers and find the missing probability with the addition rule. Tick as many as you want and set how many of each, or let it spread them evenly.
Adding without taking the overlap off. If both can happen at once, straight addition counts that case twice and the answer can even come out above 1, which is a signal something has gone wrong.