True or False? On a tree diagram, the branches for the second event always carry the same probabilities whichever branch you arrived along.

False. On a tree diagram the second set of branches can carry different probabilities depending on which branch came before, and that is precisely what tree diagrams are good at showing. So, for example , if an item is drawn and not replaced , what is left to draw from depends on what was taken first, so the two sets of second branches differ. When the probabilities are the same either way, the two events are independent.

True or False? Every branch of a tree diagram must lead on to the same number of later branches.

False. A branch stops wherever the experiment stops, so some branches lead on and others do not. So, for example , in a test that is retaken until it is passed, the fail branch leads on to another attempt but the pass branch does not, because there is nothing left to happen.

Why are you allowed to add the probabilities of several complete paths through a tree diagram?

The complete paths through a tree diagram are mutually exclusive , so adding their probabilities never counts an outcome twice: the experiment ends up on exactly one path. That is why a question asking for several different final outcomes becomes a sum. Work out each path by multiplying along it, then add the paths you want.

What two checks are built into every tree diagram?

The probabilities on each pair of branches must add up to 1. The probabilities of all the final outcomes must add up to 1. Both are worth running, because they catch different mistakes: the first finds a branch labelled wrongly, and the second finds a path left out or multiplied wrongly.

A LevelMathsCambridge (CIE)Probability & Statistics 1FlashcardsProbabilityBasic Probability

Basic Probability (Cambridge (CIE) A Level Maths: Probability & Statistics 1): Flashcards

Exam code: 9709

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FrontTree Diagrams
True or False?
On a tree diagram, the branches for the second event always carry the same probabilities whichever branch you arrived along.
BackTree Diagrams
False.
On a tree diagram the second set of branches can carry different probabilities depending on which branch came before, and that is precisely what tree diagrams are good at showing.
So, for example, if an item is drawn and not replaced, what is left to draw from depends on what was taken first, so the two sets of second branches differ.
When the probabilities are the same either way, the two events are independent.
BackTree Diagrams
The probability of a complete path is the product of the probabilities labelling its branches.
Where the second event depends on the first, the number on the second branch is already the probability of that event given what has just happened, so multiplying the labels is correct even though the two events are not independent.
So, for example, a path whose branches are labelled $0.8$ , $0.4$ and $0.8$ has probability $0.8 \times 0.4 \times 0.8 = 0.256$ .

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Cards in this collection (6)

True or False?
On a tree diagram, the branches for the second event always carry the same probabilities whichever branch you arrived along.
False.
On a tree diagram the second set of branches can carry different probabilities depending on which branch came before, and that is precisely what tree diagrams are good at showing.
So, for example, if an item is drawn and not replaced, what is left to draw from depends on what was taken first, so the two sets of second branches differ.
When the probabilities are the same either way, the two events are independent.
How do you find the probability of one complete path through a tree diagram?
The probability of a complete path is the product of the probabilities labelling its branches.
Where the second event depends on the first, the number on the second branch is already the probability of that event given what has just happened, so multiplying the labels is correct even though the two events are not independent.
So, for example, a path whose branches are labelled $0.8$ , $0.4$ and $0.8$ has probability $0.8 \times 0.4 \times 0.8 = 0.256$ .
True or False?
Every branch of a tree diagram must lead on to the same number of later branches.
False.
A branch stops wherever the experiment stops, so some branches lead on and others do not.
So, for example, in a test that is retaken until it is passed, the fail branch leads on to another attempt but the pass branch does not, because there is nothing left to happen.
Why are you allowed to add the probabilities of several complete paths through a tree diagram?
The complete paths through a tree diagram are mutually exclusive, so adding their probabilities never counts an outcome twice: the experiment ends up on exactly one path.
That is why a question asking for several different final outcomes becomes a sum.
Work out each path by multiplying along it, then add the paths you want.
A contestant has three attempts to hit a target, and wins by hitting it at least once. Rather than adding the three winning paths, complete the shortcut:
$P (wins) = 1 - P (______)$
The completed shortcut is:
$P (wins) = 1 - P (misses all three)$
There are three separate paths that win and only one that loses, so the subtraction replaces three multiplications and an addition with a single calculation.
Look for this whenever a question says at least one, because that phrasing almost always means the losing outcome is a single path.
What two checks are built into every tree diagram?
The probabilities on each pair of branches must add up to 1.
The probabilities of all the final outcomes must add up to 1.
Both are worth running, because they catch different mistakes: the first finds a branch labelled wrongly, and the second finds a path left out or multiplied wrongly.

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