True or False? A two-way table is used to compare two types of characteristics .

True. A two-way table is used to compare two types of characteristics . E.g. school year group and favourite genre of movie.

How do you construct a two-way table from information given in words?

Identify the two characteristics, e.g. favourite colours, gender Use rows for one characteristic and columns for the other Add an extra row and column for marginal totals Red Blue Yellow Total Male Female Total

True or false? The numbers needed to complete a two-way table will always be given explicitly in a question.

False. When completing a two-way table, some values can be filled in directly from the question information , but some values will need to be worked out . E.g. you may need to subtract other values in a row from the row total to find a missing value.

How can you double-check your answers when completing a two-way table ?

You can double-check your answers when completing a two-way table by making sure that all row and column totals add up correctly, and that they match the grand total .

True or False? Frequency trees are usually used when each characteristic has only two possible outcomes of interest.

True. Frequency trees are usually used when each characteristic has only two possible outcomes of interest.

What is the purpose of the ' bubble ' at the start of a frequency tree ?

The bubble at the start of a frequency tree contains the total frequency of all outcomes.

True or False? The order of characteristics on the branches of a frequency tree matters.

False. The order of characteristics on the branches of a frequency tree does not matter . Strictly speaking, it does not matter which set of branches has which characteristic.

True or False? Frequencies in a frequency tree always increase from left to right.

False. Frequencies in a frequency tree do not always increase from left to right. In general, the values decrease from left to right as the total frequency is broken down in a frequency tree.

What is a quick check to ensure a frequency tree is completed correctly ?

A quick check to ensure a frequency tree is completed correctly is to make sure the values in the bubbles at the end of each set of branches add up to the total frequency .

What does the first set of branches in a frequency tree represent?

The first set of branches in a frequency tree breaks down the total frequency into the frequencies for the outcomes of the first characteristic.

True or False? Frequency trees can easily handle three or more characteristics.

False. Frequency trees can not easily handle more than three characteristics While it is possible to have three or more characteristics in a frequency tree, such diagrams would quickly become large and cumbersome.

True or False? The rectangle drawn around a Venn diagram represents the universal set.

True. The rectangle stands for the universal set , and each circle drawn inside it stands for one set. Two circles are drawn overlapping only where the sets share elements.

How do you find a probability from a Venn diagram that shows frequencies?

Add together the frequencies in the regions you want, then divide by the total frequency. If the diagram lists individual elements instead of frequencies, count the elements you want and divide by the total number of elements.

Where do the items that are in neither set go on a Venn diagram?

Inside the rectangle but outside both circles. They still count towards the total, so they must be included in the denominator when you work out a probability.

GCSEMathsEdexcelFoundationFlashcardsProbabilitySimple Probability Diagrams

Simple Probability Diagrams (Edexcel GCSE Maths: Foundation): Flashcards

Exam code: 1MA1

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FrontTwo-Way Tables
True or False?
A two-way table is used to compare two types of characteristics.
FrontTwo-Way Tables
How do you construct a two-way table from information given in words?
BackTwo-Way Tables
Identify the two characteristics, e.g. favourite colours, gender
Use rows for one characteristic and columns for the other
Add an extra row and column for marginal totals
Red
Blue
Yellow
Total
Male
Female
Total

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Cards in this collection (26)

True or False?
A two-way table is used to compare two types of characteristics.
True.
A two-way table is used to compare two types of characteristics.
E.g. school year group and favourite genre of movie.
How do you construct a two-way table from information given in words?
1. Identify the two characteristics, e.g. favourite colours, gender
2. Use rows for one characteristic and columns for the other
3. Add an extra row and column for marginal totals
Red
Blue
Yellow
Total
Male
Female
Total
True or false?
The numbers needed to complete a two-way table will always be given explicitly in a question.
False.
When completing a two-way table, some values can be filled in directly from the question information, but some values will need to be worked out.
E.g. you may need to subtract other values in a row from the row total to find a missing value.
How can you double-check your answers when completing a two-way table?
You can double-check your answers when completing a two-way table by making sure that all row and column totals add up correctly, and that they match the grand total.
How can the probability of an event occurring be worked out from a two-way table?
E.g. what is the probability that a randomly selected student's favourite subject is Physics?
Biology
Physics
Chemistry
Total
Year 7
12
8
10
30
Year 8
8
13
6
27
Total
20
21
16
57
The probability of a particular event occurring can be worked out by finding the number of successes by the total number.
E.g. the probability that a student's favourite subject is Physics is $\frac{21}{57}$ .
Biology
Physics
Chemistry
Total
Year 7
12
8
10
30
Year 8
8
13
6
27
Total
20
21
16
57
What is a frequency tree?
A frequency tree is a diagram that shows the frequencies associated with two characteristics of a set of data.
E.g. The below frequency tree shows the number of ducks and swans, broken down by male and female.
True or False?
Frequency trees are usually used when each characteristic has only two possible outcomes of interest.
True.
Frequency trees are usually used when each characteristic has only two possible outcomes of interest.
What is the purpose of the 'bubble' at the start of a frequency tree?
The bubble at the start of a frequency tree contains the total frequency of all outcomes.
True or False?
The order of characteristics on the branches of a frequency tree matters.
False.
The order of characteristics on the branches of a frequency tree does not matter.
Strictly speaking, it does not matter which set of branches has which characteristic.
True or False?
Frequencies in a frequency tree always increase from left to right.
False.
Frequencies in a frequency tree do not always increase from left to right.
In general, the values decrease from left to right as the total frequency is broken down in a frequency tree.
What is a quick check to ensure a frequency tree is completed correctly?
A quick check to ensure a frequency tree is completed correctly is to make sure the values in the bubbles at the end of each set of branches add up to the total frequency.
What does the first set of branches in a frequency tree represent?
The first set of branches in a frequency tree breaks down the total frequency into the frequencies for the outcomes of the first characteristic.
True or False?
Frequency trees can easily handle three or more characteristics.
False.
Frequency trees can not easily handle more than three characteristics
While it is possible to have three or more characteristics in a frequency tree, such diagrams would quickly become large and cumbersome.
Define a set.
A set is a collection of elements, which may be numbers, letters, coordinates or anything else.
Its elements are listed inside curly brackets, so the factors of 6 form the set $\{1, 2, 3, 6\}$ .
What is the universal set?
The universal set is the set of everything being considered, written $E$ .
If a question is only concerned with the factors of 24, then $E$ is the set of those factors and nothing else.
What does $n (A)$ mean?
It is the number of elements in set $A$ .
If $A = \{1, 4, 9\}$ then $n (A) = 3$ .
What does $x \in A$ mean?
That $x$ is an element of the set $A$ , meaning $x$ is one of the things in $A$ .
If $A = \{2, 6, 12\}$ then $6 \in A$ is true.
What does $A \cap B$ mean?
The intersection of $A$ and $B$ , which is the set of elements that are in both sets.
On a Venn diagram it is the region where the two circles overlap.
What does $A \cup B$ mean?
The union of $A$ and $B$ , which is the set of elements in at least one of the sets.
This includes everything in the overlap, but each element is written only once.
True or False?
The rectangle drawn around a Venn diagram represents the universal set.
True.
The rectangle stands for the universal set, and each circle drawn inside it stands for one set.
Two circles are drawn overlapping only where the sets share elements.
For $A = \{2, 6, 12, 14, 28\}$ and $B = \{7, 14, 21, 28, 35\}$ , complete the two statements:
$A \cap B =______$
$n (A) =______$
The completed statements are:
$A \cap B = \{14, 28\}$
$n (A) = 5$
Only 14 and 28 appear in both lists, and $A$ has five elements altogether.
How do you find a probability from a Venn diagram that shows frequencies?
Add together the frequencies in the regions you want, then divide by the total frequency.
If the diagram lists individual elements instead of frequencies, count the elements you want and divide by the total number of elements.
True or False?
The probability of being in $A$ but not $B$ uses the whole of the $A$ circle.
False.
The overlap must be left out, because those elements are in $B$ as well.
Only the part of the $A$ circle lying outside the intersection counts.
10 people have a cat, 8 people have a dog, and 6 people have both. Complete the numbers for the Venn diagram:
Cat but not dog: $______$
Dog but not cat: $______$
The completed numbers are:
Cat but not dog: 4
Dog but not cat: 2
The 6 people who have both are already counted within the 10 and within the 8, so they are subtracted from each.
Where do the items that are in neither set go on a Venn diagram?
Inside the rectangle but outside both circles.
They still count towards the total, so they must be included in the denominator when you work out a probability.
In a class of 30, 15 study Spanish and 3 of those also study German. What is the probability that a student studies Spanish but not German?
The probability is $\frac{12}{30}$ , which simplifies to $\frac{2}{5}$ .
Of the 15 studying Spanish, 3 also take German, which leaves 12 taking Spanish only.

	Biology	Physics	Chemistry	Total
Year 7	12	8	10	30
Year 8	8	13	6	27
Total	20	21	16	57

	Biology	Physics	Chemistry	Total
Year 7	12	8	10	30
Year 8	8	13	6	27
Total	20	21	16	57

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