Define an experiment in the context of probability.

In probability, an experiment is a repeatable activity that has a result that can be observed or recorded.

Define a trial in the context of probability.

In probability, a trial is one of the repeats of an experiment.

Define an outcome in the context of probability.

In probability, an outcome is a possible result of a trial.

Define an event in the context of probability.

In probability, an event is an outcome or a collection of outcomes.

Define sample space .

A sample space is the set of all possible outcomes of an experiment. It may be a list or a grid showing all the possible outcomes.

True or False? Probabilities can only be expressed as fractions.

False. Probabilities can be expressed as fractions, decimals or percentages.

Define mutually exclusive events .

Mutually exclusive events are events that cannot both happen at the same time.

True or False? You can always use a sample space grid to represent all possible outcomes.

False. When combining more than two things, you may need to go back to listing outcomes instead of using a grid.

How do you calculate probabilities using a sample space?

Count the possibilities you want, then divide by the total number of possibilities in the sample space.

What is a condition for using the counting method to calculate probabilities?

All possibilities in the sample space must be equally likely.

What is conditional probability ?

Conditional probability is the probability of an event occurring given that another event has occurred.

Define relative frequency in the context of probability.

In probability, relative frequency (also called experimental probability) is used to estimate probabilities from experimental data.

How do you calculate relative frequency?

Relative frequency is calculated as the number of successful outcomes divided by the total number of trials.

When is relative frequency used?

Relative frequency is used when theoretical probabilities are unavailable or not possible to calculate, or to test if a situation is fair or biased.

What is a condition for using relative frequency to estimate probabilities?

To use relative frequency to estimate probabilities, there must be an equal chance of 'success' on each trial. I.e., trials are independent.

True or False? Calculating a relative frequency lets you know the exact probability.

False. Relative frequency only provides an estimate for the true (or theoretical) probability.

Define expected frequency in the context of probability.

Expected frequency refers to the number of times a particular outcome is expected to occur when repeating a trial numerous times.

True or False? If an experiment is repeated many times, the number of occurrences of an event will always be exactly equal to the expected frequency.

False. The number of occurrences averages out to the expected frequency over many repetitions, but may not be exactly equal.

True or false? Relative frequency and expected frequency can both take on any positive value.

False. Expected frequency can in theory take on any positive numerical value. But relative frequency is an estimate of a probability, so must be between 0 and 1.

True or false? A larger number of trials should give a more accurate result for relative frequency than a smaller number of trials.

True. Usually a relative frequency calculated from a large number of trials is more reliable than one calculated from a small number of trials.

What are systematic listing strategies when calculating probabilities?

Systematic listing strategies are ways of writing out all possible combinations or arrangements of items in an organised way, without missing any.

Why are systematic listing strategies useful?

Systematic listing strategies help ensure that no options are missed when listing all possible outcomes.

How could you use a systematic listing strategy to list all the possible ways to arrange the letters A, B and C?

For listing arrangements of letters A, B, C: Fix A first, and list ABC, ACB Fix B next, and list BAC, BCA Fix C last, and list CAB, CBA The six arrangements are ABC, ACB, BAC, BCA, CAB and CBA.

True or False? Systematic listing strategies can only be used for arranging letters.

False. Systematic listing strategies can be applied to arrangements of any items, not just letters.

How can you simplify the information given in a question to help when using systematic listing strategies?

Simplifying the information by assigning letters or symbols to each item mentioned in the question can make the listing process easier.

True or False? Systematic listing strategies only work for a small number of items.

False. Systematic listing strategies can be used for any number of items, although it may become more tedious with a larger number of items.

Why is it better to use a systematic listing strategy, rather than an unsystematic list?

Systematic listing strategies help ensure completeness and avoid missing any possibilities, whereas unsystematic listing risks missing options.

IGCSEMaths A: HigherEdexcelFlashcards

Probability Toolkit (Edexcel IGCSE Maths A)

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Define an experiment in the context of probability.

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Cards in this collection (32)

Define an experiment in the context of probability.
In probability, an experiment is a repeatable activity that has a result that can be observed or recorded.
Define a trial in the context of probability.
In probability, a trial is one of the repeats of an experiment.
Define an outcome in the context of probability.
In probability, an outcome is a possible result of a trial.
Define an event in the context of probability.
In probability, an event is an outcome or a collection of outcomes.
What is $P (A)$ ?
$P (A)$ is the notation for the probability of event A occurring.
Define sample space.
A sample space is the set of all possible outcomes of an experiment.
It may be a list or a grid showing all the possible outcomes.
True or False?
Probabilities can only be expressed as fractions.
False.
Probabilities can be expressed as fractions, decimals or percentages.
Define mutually exclusive events.
Mutually exclusive events are events that cannot both happen at the same time.
What is the complement of event A?
The complement of event A is the event where event A does not happen. It is denoted by $A^{'}$ .
State an equation connecting $P (A)$ and $P (A^{'})$ .
The key equation connecting $P (A)$ and $P (A^{'})$ is $P (A) + P (A^{'}) = 1$ .
It can be rearranged as $P (A^{'}) = 1 - P (A)$ or $P (A) = 1 - P (A^{'})$ .
True or False?
You can always use a sample space grid to represent all possible outcomes.
False.
When combining more than two things, you may need to go back to listing outcomes instead of using a grid.
How do you calculate probabilities using a sample space?
Count the possibilities you want, then divide by the total number of possibilities in the sample space.
What is a condition for using the counting method to calculate probabilities?
All possibilities in the sample space must be equally likely.
True or False?
There are only two possibilities in a lottery, 'win' and 'lose'. So the probability of winning is $\frac{1}{2}$ .
False.
You cannot use the counting method here, because the outcomes 'win' and 'lose' are not equally likely.
What is conditional probability?
Conditional probability is the probability of an event occurring given that another event has occurred.
Define relative frequency in the context of probability.
In probability, relative frequency (also called experimental probability) is used to estimate probabilities from experimental data.
How do you calculate relative frequency?
Relative frequency is calculated as the number of successful outcomes divided by the total number of trials.
When is relative frequency used?
Relative frequency is used when theoretical probabilities are unavailable or not possible to calculate, or to test if a situation is fair or biased.
What is a condition for using relative frequency to estimate probabilities?
To use relative frequency to estimate probabilities, there must be an equal chance of 'success' on each trial. I.e., trials are independent.
True or False?
Calculating a relative frequency lets you know the exact probability.
False.
Relative frequency only provides an estimate for the true (or theoretical) probability.
Define expected frequency in the context of probability.
Expected frequency refers to the number of times a particular outcome is expected to occur when repeating a trial numerous times.
State the equation for the expected frequency of an event with probability $p$ , if the experiment is repeated $n$ times.
If the probability of a particular outcome is $p$ and there are $n$ trials, the expected frequency is $n p$ (number of trials times probability of event occurring).
True or False?
If an experiment is repeated many times, the number of occurrences of an event will always be exactly equal to the expected frequency.
False.
The number of occurrences averages out to the expected frequency over many repetitions, but may not be exactly equal.
True or false?
Relative frequency and expected frequency can both take on any positive value.
False.
Expected frequency can in theory take on any positive numerical value.
But relative frequency is an estimate of a probability, so must be between 0 and 1.
True or false?
A larger number of trials should give a more accurate result for relative frequency than a smaller number of trials.
True.
Usually a relative frequency calculated from a large number of trials is more reliable than one calculated from a small number of trials.
What are systematic listing strategies when calculating probabilities?
Systematic listing strategies are ways of writing out all possible combinations or arrangements of items in an organised way, without missing any.
Why are systematic listing strategies useful?
Systematic listing strategies help ensure that no options are missed when listing all possible outcomes.
How could you use a systematic listing strategy to list all the possible ways to arrange the letters A, B and C?
For listing arrangements of letters A, B, C:
- Fix A first, and list ABC, ACB
- Fix B next, and list BAC, BCA
- Fix C last, and list CAB, CBA
The six arrangements are ABC, ACB, BAC, BCA, CAB and CBA.
True or False?
Systematic listing strategies can only be used for arranging letters.
False.
Systematic listing strategies can be applied to arrangements of any items, not just letters.
How can you simplify the information given in a question to help when using systematic listing strategies?
Simplifying the information by assigning letters or symbols to each item mentioned in the question can make the listing process easier.
True or False?
Systematic listing strategies only work for a small number of items.
False.
Systematic listing strategies can be used for any number of items, although it may become more tedious with a larger number of items.
Why is it better to use a systematic listing strategy, rather than an unsystematic list?
Systematic listing strategies help ensure completeness and avoid missing any possibilities, whereas unsystematic listing risks missing options.

1. Numbers & the Number System

2. Equations, Formulae & Identities

3. Sequences, Functions & Graphs

4. Geometry & Trigonometry

5. Vectors & Transformation Geometry

6. Statistics & Probability