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 .

GCSEMathsEdexcelFoundationFlashcardsProbabilityTree Diagrams & Combined Probability

Tree Diagrams & Combined Probability (Edexcel GCSE Maths: Foundation): Flashcards

Exam code: 1MA1

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Define a probability tree diagram.

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Cards in this collection (11)

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:
$P (A or B) = P (A) + P (B)$ .

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