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 .

IGCSEMathsEdexcelMaths A (Modular)Higher Unit 1FlashcardsStatistics & ProbabilityProbability Diagrams: Venn & Tree Diagrams

Probability Diagrams: Venn & Tree Diagrams (Edexcel IGCSE Maths A (Modular))

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FrontProbabilities from Venn Diagrams
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.

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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.

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