AQA · Mathematics · 8300
GCSE Maths: Probability: tree diagrams
Probability · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Probability: tree diagrams (Corbettmaths Video 252), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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In a tree diagram, how do you calculate the probability of a sequence of independent events?
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Multiply the probabilities along the branches of the path representing that sequence.
What does "at least one" mean when calculating probability?
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One or more occurrences. It's often easier to calculate as 1 minus the probability of none occurring.
When a sweet is taken from a bag, its flavour recorded, and then put back before the second selection, what type of probability scenario is this?
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Sampling with replacement. The probabilities remain the same for each draw because the sweet is returned to the bag.
In a probability tree diagram, what must all probabilities from branches leaving a single point sum to?
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They must sum to 1, because they represent all possible outcomes from that point.
When sampling without replacement from a bag of counters, how do the probabilities change for the second draw?
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The total number of items decreases by 1, and the number of the selected type also decreases by 1 if that type was chosen first, changing the probability fractions.
In a two-stage tree diagram, how do you find the probability of exactly one success occurring?
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Add the probability of success then failure to the probability of failure then success.
If a tree diagram shows conditional probabilities that depend on the outcome of a previous event, are the events independent?
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No, they are dependent events. The probability of the second event changes based on what happened in the first event.
How can you calculate the expected number of times an outcome occurs over multiple trials?
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Multiply the probability of the outcome by the number of trials.
To find the probability of getting two bad apples when selecting without replacement, you multiply the probability of getting a bad apple first by the probability of getting a bad apple ?.
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second given one was already removed
When using a probability tree diagram to find the total probability of an event that can occur in multiple ways, what operation do you perform?
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Add the probabilities of all the paths that lead to that event.
If probabilities for all outcomes on a spinner are given in terms of x, what must the sum of all probabilities equal?
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1 (or 100%). This allows you to solve for x.
If you know P(A and B) and P(A) for independent events, how do you find P(B)?
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Divide: P(B) = P(A and B) ÷ P(A). For independent events, P(A and B) = P(A) × P(B).
When calculating expected profit or loss from a probability game, what two values do you need for each outcome?
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The probability of the outcome and the financial value (profit or loss) associated with it.
In a tree diagram, when are the probabilities on the second set of branches the same as those on the first set?
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When the events are independent or when sampling with replacement.
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