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? To find the probability of A and B using a probability tree diagram, you add the probabilities on the branches fo r A and B .

False. To find the probability of A and B using a probability tree diagram, you do not add the probabilities on the branches for A and B . To find the probability of A and B , you multiply along the branches.

True or False? The probabilities on all of the branches in a probability tree diagram should add up to 1 .

False. The probabilities on all of the branches in a probability tree diagram should not add up to 1 . The probabilities on any set of branches (usually a pair) should add up to 1 .

True or False? The sum of the probabilities of all of the final outcomes on a probability tree diagram should be equal to 1 .

True. The sum of the probabilities of all of the final outcomes on a probability tree diagram should be equal to 1 .

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)ExtendedFlashcardsProbabilityProbability Diagrams (Tree & Venn Diagrams)

Probability Diagrams (Tree & Venn Diagrams) (Cambridge (CIE) IGCSE Maths)

Flashcards

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Front
True or False?
A two-way table is used to compare two types of characteristics.
Front
How do you construct a two-way table from information given in words?
Back
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 (22)

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
Describe how to find $P (A)$ from a Venn diagram that shows sets $A$ and $B$ .
E.g. find $P (A)$ from the Venn diagram.
$P (A)$ is the probability of being in set $A$ .
This is the number inside the full circle of set $A$ divided by the total number of the whole Venn diagram, e.g. $P (A) = \frac{8 + 2}{8 + 2 + 15 + 7} = \frac{10}{32}$ .
Describe how to find $P (A \cap B)$ from a Venn diagram that shows sets $A$ and $B$ .
E.g. find $P (A \cap B)$ from the Venn diagram.
$P (A \cap B)$ is the probability of being in the intersection of set $A$ and set $B$ .
This is the value inside the overlapping region of set $A$ and set $B$ divided by the total number of the whole Venn diagram, e.g. $P (A \cap B) = \frac{2}{8 + 2 + 15 + 7} = \frac{2}{32}$ .
True or False?
If $A$ and $B$ are mutually exclusive, then $P (A \cap B) = 0$ .
True.
If $A$ and $B$ are mutually exclusive, then $P (A \cap B) = 0$ .
On a Venn diagram, if $A$ and $B$ are mutually exclusive then their circles do not overlap (they cannot both happen at the same time).
This makes being in the intersection impossible, so $P (A \cap B) = 0$ .
True or False?
To find $P (A \cup B)$ you need to double-count the numbers in the intersection (overlap) as they occur twice.
False.
To find $P (A \cup B)$ you do not double-count the numbers in the intersection $A \cap B$ , you just count them once.
Describe which region on a Venn diagram is required to calculate $P (A \cap B \cap C)$ .
E.g. find $P (A \cap B \cap C)$ from the Venn diagram.
The region required to calculate $P (A \cap B \cap C)$ is the one that is the overlap of all three sets $A$ , $B$ and $C$ . E.g. $P (A \cap B \cap C) = \frac{3}{5 + 2 + 11 + 6 + 3 + 1 + 9 + 8} = \frac{3}{45}$ .
True or False?
On a Venn diagram showing sets $A$ and $B$ , the region required to calculate $P (A')$ is the part of set $B$ that does not overlap $A$ .
False.
On a Venn diagram showing sets $A$ and $B$ , the region required to calculate $P (A')$ is anything that is outside the circle of $A$ , e.g.
On a Venn diagram showing sets $A$ and $B$ , explain how to calculate $P (A | B)$ .
E.g. find $P (A | B)$ from the Venn diagram.
$P (A | B)$ is a conditional probability meaning the probability of being in $A$ , given that you are in $B$ . Therefore the probability is out of set $B$ only.
The only part of set $A$ in set $B$ is $A \cap B$ , so divide the number in $A \cap B$ by the total number in $B$ , e.g. $P (A | B) = \frac{2}{2 + 15} = \frac{2}{17}$ .
True or False?
To find the probability of A and B using a probability tree diagram, you add the probabilities on the branches for A and B.
False.
To find the probability of A and B using a probability tree diagram, you do not add the probabilities on the branches for A and B.
To find the probability of A and B, you multiply along the branches.
True or False?
The probabilities on all of the branches in a probability tree diagram should add up to 1.
False.
The probabilities on all of the branches in a probability tree diagram should not add up to 1.
The probabilities on any set of branches (usually a pair) should add up to 1.
True or False?
The sum of the probabilities of all of the final outcomes on a probability tree diagram should be equal to 1.
True.
The sum of the probabilities of all of the final outcomes on a probability tree diagram should be equal to 1.
A tree diagram is used to represent two events, A and B, where each event has three possible outcomes, 1, 2 and 3.
How many possible final outcomes are there?
For a tree diagram used to represent two events, where each events has three possible outcomes, there are nine possible final outcomes (3² = 9).
A tree diagram is used to represent three tennis matches, where each event has two possible outcomes: player A winning or player B winning.
How many possible final outcomes are there?
A tree diagram is used to represent three tennis matches, where each event has two possible outcomes: player A winning or player B winning.
There are eight possible final outcomes (2³ = 8).
The eight outcomes are AAA, AAB, ABA, ABB, BAA, BAB, BBA, BBB.
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:
$P (A or B) = P (A) + P (B)$ .