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? 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.

Define a probability tree diagram .

A probability tree diagram shows the outcomes of two or more experiments in order, with a probability written on each branch . Each complete path from left to right represents one combined outcome.

How do you use a tree diagram to find the probability of a particular pair of outcomes?

Multiply the probabilities along the branches of that path, working from left to right. If more than one path gives what you want, work each path out separately and then add the results together.

What is the quickest way to find the probability of at least one outcome?

Find the probability that it happens none of the time, then subtract that from 1. Adding up every path that contains at least one takes far longer and is easier to get wrong.

True or False? You should simplify each fraction as you multiply along the branches.

False. Leaving the fractions unsimplified keeps them over the same denominator . That makes the final step of adding several paths together much easier.

True or False? The sum of all probabilities is 1 .

True. As long as the possibilities considered are all mutually exclusive (non-overlapping), then the sum of all probabilities is 1 .

IGCSEMathsCambridge (CIE)CoreFlashcardsProbabilitySet Notation & Probability Diagrams

Set Notation & Probability Diagrams (Cambridge (CIE) IGCSE Maths: Core): Flashcards

Exam code: 0580 & 0980

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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 (29)

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
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.
Define a probability tree diagram.
A probability tree diagram shows the outcomes of two or more experiments in order, with a probability written on each branch.
Each complete path from left to right represents one combined outcome.
How do you use a tree diagram to find the probability of a particular pair of outcomes?
Multiply the probabilities along the branches of that path, working from left to right.
If more than one path gives what you want, work each path out separately and then add the results together.
True or False?
A tree diagram for two experiments, each with two outcomes, has four complete paths.
True.
Each of the two first-stage branches splits into two, giving $2 \times 2 = 4$ complete paths.
Every possible combined outcome is one of those four.
What is the quickest way to find the probability of at least one outcome?
Find the probability that it happens none of the time, then subtract that from 1.
Adding up every path that contains at least one takes far longer and is easier to get wrong.
Two sets of traffic lights show green with probabilities $\frac{5}{7}$ and $\frac{8}{9}$ . Complete the working for both showing red:
$\frac{2}{7} \times______=______$
The completed working is:
$\frac{2}{7} \times \frac{1}{9} = \frac{2}{63}$
Each red probability is found by subtracting the matching green probability from 1.
True or False?
You should simplify each fraction as you multiply along the branches.
False.
Leaving the fractions unsimplified keeps them over the same denominator.
That makes the final step of adding several paths together much easier.
What does AND mean for combined probabilities?
AND means multiply ( $\times$ ) and is used for independent events to find the probability of both events occurring.
E.g. the probability of events A and B occurring is $P (A) \times P (B)$ .
What does OR mean for combined probabilities?
OR means add (+) and is used for mutually exclusive events to find the probability of one event or the other event occurring.
E.g. the probability of either event A and/or event B occurring is $P (A) + P (B)$ .
True or False?
The sum of all probabilities is 1.
True.
As long as the possibilities considered are all mutually exclusive (non-overlapping), then the sum of all probabilities is 1.
State the equation for the probability of two independent events, $A$ and $B$ , occurring together.
If $A$ and $B$ are independent events, then the probability of both events occurring is:
$P (A and B) = P (A) \times P (B)$ .
State the equation for the probability of one or the other of two mutually exclusive events, $A$ and $B$ , occurring.
If $A$ and $B$ are mutually exclusive events, then the probability of one or the other of them occurring is:
$P (A or B) = P (A) + P (B)$ .

	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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