Precalculus probability of compound events worksheet
Three rules that cover most of the topic: and means multiply, or means add and then take off the overlap, and drawing without replacement changes the second fraction.
A bag has 4 red and 6 blue counters. Two are drawn without replacement. Find P(both red).
The first draw is 4 out of 10.
One red is gone, so the second is 3 out of 9.
Multiply.
The answer is 152.
Where students go wrong
Using the same fraction twice when there is no replacement. The second draw happens in a smaller bag with one fewer of whatever you took, and forgetting that is the single most common error on this topic.
Also called independent events, dependent events, mutually exclusive events or compound probability.
What you can put on this worksheet
Independent events: both the same
A bag has 4 red and 4 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).→ 41
Independent events: one of each
A bag has 4 red and 4 blue counters. One is drawn, replaced, then another is drawn. Find P(one of each color).→ 21
Dependent events: both the same
A bag has 4 red and 4 blue counters. Two are drawn without replacement. Find P(both red).→ 143
Dependent events: one of each
A bag has 4 red and 4 blue counters. Two are drawn without replacement. Find P(one of each color).→ 74
One event or the other
A 6-sided die is rolled. Find P(greater than 3 or less than 3).→ 65
Probability with combinations
A box has 3 winning tickets out of 10. 2 are drawn at once. Find P(both are winners).→ 151
Experimental probability
A spinner was spun 40 times and landed on red 22 times. Find the experimental probability→ 2011
Questions about these worksheets
Yes. Every probability of compound 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 probability of compound 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 two 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 7: independent events: both the same, independent events: one of each, dependent events: both the same, dependent events: one of each, one event or the other, probability with combinations and experimental probability. Tick as many as you want and set how many of each, or let it spread them evenly.
Using the same fraction twice when there is no replacement. The second draw happens in a smaller bag with one fewer of whatever you took, and forgetting that is the single most common error on this topic.