AQA · Mathematics · 8300
GCSE Maths: Probability: sample space
Probability · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Probability: sample space (Corbettmaths Video 246), 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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What is a sample space in probability?
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The set of all possible outcomes of a probability experiment.
When rolling two fair six-sided dice and adding the scores, which sum is most likely?
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7. It has the most combinations (6 ways: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1).
When rolling two fair six-sided dice and adding the scores, which sums are least likely?
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2 and 12. Each has only one way to occur (1+1 and 6+6 respectively).
Why is a sample space diagram (table) useful in probability?
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It systematically shows all possible outcomes, making it easier to count favorable outcomes and calculate probabilities.
In a probability sample space with equally likely outcomes, probability equals ?.
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number of favorable outcomes divided by total number of outcomes
When two independent random events occur together, how do you find the total number of possible outcomes?
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Multiply the number of outcomes from each event. For example, rolling a die (6 outcomes) and flipping a coin (2 outcomes) gives 6 × 2 = 12 total outcomes.
In a sample space where outcomes are NOT equally likely, what additional information do you need to calculate probabilities?
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The probability of each individual outcome. You cannot simply count outcomes; you must weight them by their probabilities.
When calculating expected profit from a probability game, what formula do you use?
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Expected profit = (number of times played × cost per play) - (number of wins × payout per win). Use probability to estimate wins.
When two fair six-sided dice are multiplied together, how many of the 36 outcomes produce an odd number?
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9 outcomes. Both dice must show odd numbers (1, 3, or 5), giving 3 × 3 = 9 combinations.
What does 'at random' mean in probability?
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Each outcome has an equal chance of being selected; the selection is unbiased.
When finding probability from a sample space table, what is the formula?
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Probability = (number of favorable outcomes) / (total number of possible outcomes)
If you spin two fair spinners and add the results, how many total outcomes are there if spinner 1 has 4 sections and spinner 2 has 3 sections?
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12 outcomes (4 × 3 = 12)
When creating a sample space for two dice, each numbered 1 to 6, how many total outcomes are possible?
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36 outcomes (6 × 6 = 36)
When rolling a die and flipping a coin, how many total outcomes exist?
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12 outcomes (6 outcomes from die × 2 outcomes from coin = 12)
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