AQA · Mathematics · 8300
GCSE Maths: Probability: basic
Probability · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Probability: basic (Corbettmaths Video 245), 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 the probability of rolling a specific number (e.g., 4) on a fair six-sided dice?
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1/6
On a fair six-sided dice, what is the probability of rolling a number less than 7?
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1 (or certain). Every possible outcome on a six-sided dice is less than 7.
What is the probability of rolling an odd number on a fair six-sided dice?
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1/2 (or 0.5). Three outcomes (1, 3, 5) out of six are odd.
What is the probability of rolling a 10 on an ordinary six-sided dice?
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0 (or impossible). A six-sided dice only has outcomes 1 through 6.
If the probability of selecting a green pen is 0.6, what is the probability of selecting a red pen when only red and green pens are in the box?
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0.4. Probabilities of all outcomes must sum to 1, so P(red) = 1 - 0.6 = 0.4.
A bag contains 10 yellow counters, 5 orange counters, and 4 white counters. What is the probability of selecting an orange counter at random?
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5/19. There are 5 orange counters out of a total of 19 counters.
A bag contains 50 sweets: 13 lemon and the rest strawberry. What is the probability of selecting a strawberry sweet at random?
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37/50. There are 50 - 13 = 37 strawberry sweets out of 50 total.
A disc is chosen at random from discs numbered 1 to 10. What is the probability of selecting a square number?
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3/10. The square numbers from 1 to 10 are 1, 4, and 9 (three outcomes out of ten).
A disc is chosen at random from discs numbered 1 to 10. What is the probability of selecting a prime number?
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4/10 (or 2/5). The prime numbers from 1 to 10 are 2, 3, 5, and 7 (four outcomes out of ten).
What is the formula for probability?
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Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
If an event is impossible, what is its probability?
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0. For example, picking a green pen from a box containing only blue, black, and red pens has probability 0.
How many prime numbers less than 20 are even?
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Only 1 (the number 2). It is the only even prime number.
What is the sum of all probabilities for all possible outcomes of an event?
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1 (or 100%). All probabilities must add up to 1 because one of the outcomes must occur.
If the probability of choosing a yellow rose is 0.1 and the probability of choosing a white rose is 0.2, what is the probability of choosing either yellow or white?
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0.3. For mutually exclusive events, add the probabilities: 0.1 + 0.2 = 0.3.
If the probabilities of choosing yellow, white, and red roses sum to 1, and P(yellow) = 0.1 and P(white) = 0.2, what is P(red)?
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0.7. Since all probabilities must sum to 1: P(red) = 1 - 0.1 - 0.2 = 0.7.
If 8 out of 60 cards have a star, what is the probability of not picking a star?
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52/60 or 13/15. There are 52 cards without stars out of 60 total.
The probability of an event NOT happening is ?.
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1 minus the probability of it happening
A bag has 400 counters: 92 yellow and P(brown) = 0.13. How many green counters are there?
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256. Brown counters = 400 × 0.13 = 52. Green = 400 - 92 - 52 = 256.
If the probability of red, green, white, and pink counters must sum to 1, and P(pink) = 0.15, P(green) = 0.25, what do P(red) and P(white) sum to?
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0.6. Since 1 - 0.15 - 0.25 = 0.6, the remaining probabilities must sum to 0.6.
If P(red) is twice P(white) and they sum to 0.6, what is P(red)?
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0.4. Let P(white) = x, then P(red) = 2x. So 2x + x = 0.6, giving x = 0.2 and P(red) = 0.4.
For a biased coin with probability of heads = 3/20, what is the probability of tails?
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17/20. Since probabilities sum to 1, P(tails) = 1 - 3/20 = 17/20.
If 300 raffle tickets are sold at £3 each with prize probability 0.2 and each prize costs £8, what is the expected total prize cost?
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£480. Expected number of prizes = 300 × 0.2 = 60. Total cost = 60 × £8 = £480.
To find the number of people WITHOUT a characteristic when given the probability WITH it, what calculation do you use?
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Multiply the total number by (1 - probability). This gives the expected count of people without the characteristic.
If you know several outcome probabilities but one is unknown and they must sum to 1, how do you find the missing probability?
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Subtract the sum of known probabilities from 1. The remainder is the missing probability.
If a spinner is spun 500 times and the probability of landing on 3 is 0.12, how many times would you expect it to land on 3?
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60 times. Expected frequency = number of trials × probability = 500 × 0.12 = 60.
Bowl A has 8 lemons and 6 limes. What is the probability of choosing a lime from Bowl A?
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6/14 or 3/7. There are 6 limes out of 14 total fruits (8 + 6 = 14).
If there are black pens (b), three times as many red pens (3b), and six times as many green pens (6b), what is the probability of picking red?
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3/10. Total pens = b + 3b + 6b = 10b. Red pens = 3b. Probability = 3b/10b = 3/10.
In a drawer with n black socks and 12 white socks, what expression gives the probability of selecting a white sock?
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12/(n + 12). The numerator is white socks, denominator is total socks.
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