AQA · Mathematics · 8300
GCSE Maths: Probability: OR rule
Probability · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Probability: OR rule (Corbettmaths Video 244), 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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A bag contains 10 yellow counters, 5 orange counters, and 4 white counters. What is the probability of choosing an orange counter at random?
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5/19 (or 5 out of 19). Total counters = 10 + 5 + 4 = 19. P(orange) = 5/19.
A bag contains 50 sweets: 13 are lemon flavoured and the rest are strawberry. What is the probability of picking a strawberry sweet at random?
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37/50. Number of strawberry sweets = 50 − 13 = 37. P(strawberry) = 37/50.
In a class of 30 students, 6 travel by bus and 11 travel by car. What is the probability a randomly selected student travelled by bus or by car?
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17/30. P(bus or car) = (6 + 11)/30 = 17/30.
A bag contains discs numbered 1 to 10. What is the probability of picking a square number at random?
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3/10. Square numbers from 1 to 10 are 1, 4, and 9 (three outcomes). P(square number) = 3/10.
A bag contains discs numbered 1 to 10. What is the probability of picking a prime number at random?
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4/10 or 2/5. Prime numbers from 1 to 10 are 2, 3, 5, and 7 (four outcomes). P(prime) = 4/10 = 2/5.
When a fair six-sided dice is rolled, what is the probability of getting a number less than 5?
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4/6 or 2/3. Numbers less than 5 are 1, 2, 3, and 4 (four outcomes out of six).
Thomas picks a card at random from 12 cards spelling 'MATHEMATICS'. What is the probability of picking the letter 'h'?
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1/12. There is 1 'h' among the 12 cards.
There are 12 chairs in a room and 5 are brown. What is the probability that a randomly chosen chair is brown?
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5/12. P(brown) = 5/12.
What is the probability of picking a green pen from a box that contains only blue, black, and red pens?
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0 (or impossible). The box contains no green pens.
What is the only even prime number?
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2
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 all probabilities for all possible outcomes must sum to what value?
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1 (or 100%). The total probability of all outcomes in a sample space is always 1.
If a bag has 60 cards total and 8 have stars, what is the probability of NOT picking a card with a star?
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52/60 or 13/15 (or 0.867). There are 60 - 8 = 52 cards without stars, so P(no star) = 52/60.
For mutually exclusive events A and B, P(A or B) = ?
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P(A) + P(B)
A bag contains 400 counters: 92 yellow and some brown and green. If P(brown) = 0.13, how many brown counters are there?
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52 counters. 0.13 × 400 = 52.
If probabilities must sum to 1 and you know P(rugby)=0.25, P(football)=0.4, P(hockey)=0.15, what is P(cricket)?
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0.2. Since 0.25 + 0.4 + 0.15 + P(cricket) = 1, then P(cricket) = 1 - 0.8 = 0.2
If there are 600 boys at a school and P(rugby) = 0.25, how many boys play rugby?
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150 boys. 0.25 × 600 = 150.
A bag has 200 counters with P(pink)=0.15, P(green)=0.25, and P(red)=2×P(white). How many counters are NOT pink or green?
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120 counters. P(not pink or green) = 1 - 0.15 - 0.25 = 0.6, so 0.6 × 200 = 120.
If the probability of an event happening is p, what is the probability it does not happen?
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1 - p. The probabilities of complementary events must sum to 1.
What formula gives the probability of selecting a specific type of item from a collection?
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P(item) = (number of that item) / (total number of items)
How do you calculate expected value for an event with multiple outcomes?
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Multiply each outcome value by its probability, then sum all the products.
How do you find the expected frequency of an outcome after n trials?
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Multiply the probability of the outcome by the number of trials (n × probability).
In a probability problem, what does 'at random' mean?
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Each item has an equal chance of being selected.
If two collections have the same probability for selecting a particular type of item, what equation can you set up?
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Set the two probability fractions equal: (count₁/total₁) = (count₂/total₂)
How do you calculate profit from a raffle if you know ticket sales, prize probability, and prize cost?
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Profit = (total ticket revenue) - (expected number of prizes × cost per prize). Expected prizes = tickets sold × probability of winning.
If you know the probability someone does NOT have a library card, how do you find the number without a card from a group of n people?
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Multiply n by (1 - probability of having a card), or n × P(not having card).
When expressing probability algebraically with n items of one type and a fixed number of another, what is the denominator?
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The sum of all items: n + (fixed number). For example, if n black socks and 12 white socks, denominator is n + 12.
If you know ratios between different types of items and a probability for one type, how can you find the original quantities?
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Use the ratio to express quantities in terms of a variable, then set up a probability equation and solve.
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