GED and HiSET mathematics — counting and compound probability

Probability on the GED Mathematical Reasoning test and the HiSET Mathematics test goes beyond picking one item from a bag. You are asked to count outcomes when several choices are combined, to tell whether order matters, and to find the probability of two events together, of either of two events, or of at least one success in several tries. These are also the calculations behind everyday questions: how many PIN codes a lock allows, what the chance is that a shipment contains a defect, how many ways a committee can be formed. This material practices them with workplace and household situations.

The twelve quiz questions each cover one rule. You count lunch combinations from entrees, sides and drinks, four-digit PIN codes with repeated digits, and the orders in which a driver can make five stops. You fill three different offices from eight members, then choose a three-person committee with no offices, and decide which of four situations is a combination rather than a permutation. On the probability side, you find the chance that two independent machines both work, that two raffle tickets drawn without replacement are both winners, and that a prize is one of two mutually exclusive kinds. You find the probability that at least one of three inspected items is defective by working from the complement, use the addition rule on a warehouse staff where some workers are both on the night shift and forklift-certified, and predict how many defective parts to expect in a shift.

Wrong options come from the typical mix-ups: adding choices instead of multiplying them, using a permutation for a committee, putting a ticket back when it was kept out, adding the probabilities of three tries instead of using the complement, or counting the overlap twice. Each explanation names the mix-up behind each wrong option.

The flashcards give the counting principle, factorials, the permutation and combination formulas, independent and dependent events, the complement rule, the at-least-one method, the addition rule, mutually exclusive events and expected counts.

The written work asks you to set up and explain each count or probability on paper: license plates, committees with conditions, repeated tries, drawing without replacement, overlapping groups and expected numbers. The oral exam asks one question at a time and expects you to say why you multiply, divide or subtract at each step.

The material is independent practice written by Zestly, based on the published content of the GED and HiSET mathematics tests; it is not produced or endorsed by GED Testing Service or ETS.

• Count outcomes with the fundamental counting principle, with and without repetition
• Use factorials, permutations and combinations and decide whether order matters
• Find the probability that two independent or dependent events both occur
• Find the probability of at least one success using the complement
• Apply the addition rule for mutually exclusive and overlapping events
• Predict an expected count from a rate or probability

Practice material written by Zestly, based on the published content of the GED Mathematical Reasoning test (counting techniques, probability of simple and compound events) and the HiSET Mathematics test (data analysis, probability and statistics).