Where this sits. This is one of the four shape, data, and chance families — the middle ground, where the formula sheet does most of the remembering and your job is choosing the right formula. Every family page on this site has the same eight parts, in the same order, so once you know the shape of one you know the shape of all of them. Where a part is empty, it says so.
DrillsNine drills for this family, one skill each, ten problems at a timeGo to the drills ↓How likely something is, written as a fraction, a decimal, or a percent: favorable outcomes over all outcomes. Then the probability that something does not happen, the probability of two things happening together, and counting how many ways a choice can be made — three shirts and four pairs of trousers make twelve outfits.
It is a small family, and it is the one most often left out of a study plan. That is a mistake worth correcting, because the whole of it fits in an afternoon and the test asks about it every time.
What the test asks in this family
- What probability is: favorable outcomes over all outcomesQuiz 34
- Writing it as a fraction, a decimal, or a percentQuiz 34
- Zero, one, and why an answer above 1 is always wrongQuiz 34
- The probability that something does not happenQuiz 34
- Two things happening togetherQuiz 34
- When the first draw changes the secondQuiz 34
- Counting how many ways a choice can be madeQuiz 34 · Counting Practice
- Permutations and combinations: whether the order mattersQuiz 34 · Counting Practice · The Calculator
- Probability against odds, and why they are not the sameQuiz 34
All 9 have something on this site.
Six questions across this family. It is the smallest one on the test and the one most often skipped, which makes it cheap points. Type an answer and press Check.
- A bag holds 3 red marbles, 5 blue and 4 green. You draw one without looking. What is the probability it is red? 1⁄4. Probability is the favorable outcomes over all the outcomes. There are 3 red and 12 marbles in total, so 3⁄12, which simplifies to 1⁄4. The test will take it as a fraction, a decimal or a percent — they are the same number.
- The forecast says a 30% chance of rain. What is the probability it does not rain? 70%. Something either happens or it does not, so the two probabilities always add to 1, or to 100%. If rain is 30%, no rain is 100 − 30 = 70%. Questions that ask for the probability of something not happening are usually easier taken this way round.
- Roll one fair six-sided die. What is the probability of a number greater than 4? 1⁄3. Only 5 and 6 are greater than 4, so that is 2 favorable outcomes out of 6, which is 2⁄6 = 1⁄3. Note that 4 itself does not count — “greater than” leaves it out, where “4 or more” would take it in.
- Flip a fair coin twice. What is the probability of getting heads both times? 1⁄4. For two things happening together, multiply their probabilities: 1⁄2 × 1⁄2 = 1⁄4. You can also list every outcome — HH, HT, TH, TT — and count: one of the four is two heads.
- You own 4 shirts and 3 pairs of trousers. How many different outfits can you make? 12. For each of the 4 shirts you have 3 choices of trousers, so 4 × 3 = 12. This is the counting principle, and it is just multiplication given a name: when one choice follows another, multiply the number of options.
- From the same bag — 3 red, 5 blue, 4 green — what is the probability the marble is not blue? 7⁄12. Two ways to see it. Count what is not blue: 3 red plus 4 green is 7, out of 12. Or take the blue probability away from the whole: 1 − 5⁄12 = 7⁄12. Both work, and agreeing with yourself twice is a good habit on this family.
Missed one? Quiz 34: Favorable Outcomes in Learn it just below teaches this whole family — the guide, three worked examples, ten questions, and a key that explains every answer. There is no app or worksheet for it yet.
Want more than these six questions? Flyover I asks about all fourteen families in one sitting and ends in a grid that says where to start; Flyover II asks them again later, with different questions, so you can see what has moved.
- Quiz 34Favorable OutcomesThe whole family in one lesson: what a probability is, the three ways to write it, what does not happen, two things together, and counting the ways.
One quiz covers this family, because the family is small. It teaches the topic first, works three examples, then asks ten questions and explains every answer — including why the wrong choices are tempting.
Nine short drills, one skill each, in order. Each starts with two worked examples, then gives you ten problems (or five) and the reasoning for every answer. Each one prints, with the answer key on the last page. When you get all ten right, or all five right twice in a row, the drill gets a check mark on the Drills page.
- 9.01Probability of one event, as a fraction, decimal and percent
- 9.02Probability that something does not happen
- 9.03Two events together (and) · calculator allowed
- 9.04One event or another (or) · calculator allowed
- 9.05How many times to expect it (out of 60 rolls) · calculator allowed
- 9.06Count the choices: multiply (outfits, menus)
- 9.07Arrangements where order matters · calculator allowed
- 9.08Groups where order does not matter · calculator allowed
- 9.09What happened compared with what was expected · calculator allowed
No app for this family yet.
- Counting Practice · forty problems on how many ways: multiplying the choices, putting things in a row, and whether the order matters. The last section mixes them so you have to decide. Answer key at the end. Made to print.
- Khan Academy, math · free videos and practice. Search it for basic probability, probability of compound events, counting principle. These are the clips we start from in class.
- Math Antics · short, plain videos on the basics.
- Light & Salt Learning · free GED classes online, with playlists by topic.
- Get Sum Math · GED math on video, one topic at a time.
- Kaplan GED Test Prep and the McGraw-Hill Mathematical Reasoning Workbook · look up probability and counting in the contents of either.
That is the end of the middle ground. What follows is the algebra families, five of them, a little over half the test. They start with exponents, roots, and scientific notation.