Probability Year 10 - Terminology - and Basic Calculations

Sep 28, 2026

Year 10 probability notes explain core terminology and foundational methods. It defines probability as a measure of how likely an event outcome is, using shorthand P(result), and distinguishes events, outcomes, successes, mutually exclusive results, complements, and impossible or certain outcomes. It covers numerical interpretation from 0 to 1 (and equivalent percent ranges), practical wording such as “likely,” and guidance on suitable answer forms. The notes introduce experimental vs theoretical probability, expected value, rules for combining probabilities across trials, and the use of probability trees for multi-step problems.

LanguageEnglish

CategoryExam

FormatPDF

Pages6

Reading Time15 min

AccessFree to download

Terminology

Probability measures and notation

Events, outcomes, and successes

Mutually exclusive events and complements

Numerical value and interpretation

Probability between 0 and 1

Interpreting “likely” and answer formats

Calculating simple probability

Experimental vs theoretical probability

Sampling assumptions

Expected value

Definition and dice example

Calculations with probabilities

Addition and multiplication rules

Arrangements and ignoring irrelevant differences

Probability trees

Building and labeling branches

Probability Year 10 Terminology Probability measures the chance something happens. Formally, we say it measures how likely is the outcome of an event. We write P(result) as a shorthand. An event is some measurable test, measurement or observation. Sometimes trial is used instead. The results of an event are often called its outcomes. The ones we are interested in are usually termed successes, regardless of their actual type (so having blue eyes can be a “success”) . Mutually exclusive results are the exact opposites of each other: either one or the other must happen. Mathematically, outcomes are mutually exclusive when their probabilities add to 1. The use of“not” helps with mutually exclusive events: the opposite of“rainy” is best thought of as“not rainy” rather than vague terms such as “fine”. Another term seen sometimes is “complement”. The complement is marked with a dash, ' , and so we can write that P(A) + P(A') = 1 Numerical value Probability is a number between 0 and 1. P(X) = 0 means that the result X is impossible P(X) = 1 means that the result X is certain. Many students prefer to think of probability as being from 0% to 100%, which is just the same thing expressed differently. Students need be prepared to leave descriptions such as “likely” behind. They are sometimes useful to describe what a probability value means, but they are not suitable when asked for a probability. In general “likely”means a probability of greater than 0.5, becoming very likely around 0.8. No probability can be bigger than one. If students get an answer larger than 1 then they should immediately recognise that as impossible. Usually answers may be given in any appropriate form: decimal, fraction or percentage. Percentages are the least useful because they have to be converted before any calculations are done. In general fractions are the most useful. Calculating Simple Probability Probabilities can be calculated experimentally. A number of trials are conducted (or events are measured) and Probability = ೙ೠ೘೙ೠ್೘೐ೝ್೐೚ೝ೑೚ೞೠ೑~~ ~~೟೎೎ೝ೔೐ೌೞ೗ೞೞ೐ೞ Experimental probability is only an estimate, and will change slightly each time it is measured. Theoretical probability can be calculated similarly, so long as each result (outcome) is equally likely: Probability = ೞೌೠ೗೗೎೛೎೐೚ೞೞೞೞ೑೔್ೠ೗೗೐ೝೝ೐೐ೞೞೠೠ೗೗೟೟ೞೞ When calculating theoretical probability it is important to divide up the outcomes in such a way as to make them equally likely. needs to be thought of as so that the white is 36 of the area. The probability of white is 36. The calculation of probability is expressed as a fraction because that is, in most cases, the best way to think about the concept. A probability of 0.2 means very little, but భఱ makes it much more obvious that it is one chance in five. When calculating experimental probability we ideally test the entire population. Sometimes that isnot possible because it is too difficult, too expensive etc or the population is infinite. In those cases we take a sample and work from that. The sample needs to be: – random – independent (the outcome of one trial does not affect the result of the others) – sufficiently large (how large depends on how accurate you need it) Students may notice that these conditions are the same as those we need for proper sampling for all statistics. Expected Value The expected value is the number of successes that are expected for a certain number of trials. Expected value = Probability × number of trials The expected value is basically the same as the mean (average) number of successes, except that a mean can be a decimal value, whereas an expected value is rounded because it is not possible to have a fractional success. The probability of 6 on a normal dice is = 16. If we roll the dice 20 times we calculate 16 × 20 = 3.33 sixes on average, but the expected number of sixes is 3, since you can’t get 13 of a roll. Calculations with Probabilities If

FAQs

What does P(result) mean in these notes?

P(result) is shorthand for the probability that a particular outcome of an event happens.

How do you interpret mutual exclusivity using probabilities?

Mutually exclusive outcomes are opposite cases where one or the other must happen, and their probabilities add to 1.

What is the expected value and how is it computed here?

Expected value equals Probability multiplied by the number of trials. It represents the average number of successes expected, with results rounded since fractional successes aren’t possible.

Sep 28, 2026

Uploaded by Alex Sinclair