Probability of events – Hard

Last updated: 20/07/2021
OCR GCSE Maths – Foundation Probability Probability of events – Hard
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  1. What is the probability of picking a red 2 in a deck of cards (not including jokers)?

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  2. An ice cream shop is testing out new ice cream flavours, and a number of customers try 1 flavour each. Based on the table, what is the probability that a customer tried strawberry flavour?

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  3. If a fair 6-sided dice is rolled, what is the probability it will land on a prime number?

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  4. A drawer is filled with 128 pairs of socks, they are either green or yellow. Based on the table, what is the probability that a yellow pair will be picked (as a fraction)?

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  5. A bag contains some shapes. 20x are pentagons, 17x are squares, 11x are rectangles and 2x are circles. What is the probability percentage of picking a square?

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  6. A bag contains 60 counters, 37 are black, 5 are white, 9 are brown and 9 are pink what is the probability of picking a pink?

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  7. A bag contains some balls, 23 are blue, 5 are red, 4 are brown and 8 are purple, what is the probability of picking a ball that isn’t blue?

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  8. A bag contains some pens, 14 are green, 19 are white, 45 are yellow and 22 are pink, what is the probability percentage of picking a pen that isn’t white or yellow?

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  9. What is the probability of landing on a cube number on a spinner with numbers 1-26?

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  10. There are 40 students in a class and 10 like dogs and 8 like cats. What is the probability of picking a student who doesn’t like either dogs or cats?

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  11. A bag contains 60 pens, 3x are green, 4x are purple, 3x are white. what is the probability of picking a purple?

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  12. A bag contains 30 balls, 1x are red, 2x are orange, 3x are black. what is the probability of picking a black?

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  13. A bag contains 100 shapes, 24 are triangles, 4 are squares and 7 are circles. If the rest are pentagons, what is the probability of picking a pentagon (as a percentage)?

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  14. A bag contains 30 counters, 17 are blue, 5 are orange, 3 are brown and 5 are purple, what is the probability of picking a blue counter?

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  15. A bag contains some shapes, 17 are triangles, 6 are hexagons and 3 are quadrilaterals. What is the probability of picking a quadrilateral?

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  16. A bag contains 35 counters, 11 are black, 12 are pink, 9 are red and 3 are orange, what is the probability of picking a red?

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  17. A class contains 20 girls and 10 boys. 1/4 of the girls have blue eyes and 1/2 of the boys have blue eyes. What is the probability of picking a student with blue eyes?

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  18. A bag contains 29 counters, 9 are red, 3 are orange, 2 are black. If the rest are purple, what is the probability of picking a purple?

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  19. A bag contains 1 rhombus, 3 triangles, 5 squares, 3 circles and 1 rectangle. What is the probability of picking a 4-sided shape?

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  20. A bag contains 50 counters, 20 are green, 3 are blue, 1 is black. If the rest are red what is the probability of picking a red (as a percentage)?

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  21. If a fair 6-sided dice is rolled, what is the probability it will not land on a prime number?

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  22. There is a number spinner with numbers 1-17 on it. What is the probability of picking a prime number (as a fraction)?

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  23. A boat filled with passengers arrives in the UK. Based on the tree diagram, what is the probability that those passengers will not have any dogs with them?

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  24. There is a number spinner with numbers 1-20 on it. What is the probability of picking a square number or a cube number (as a percentage)?

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  25. A shop is testing out flavours, and a number of customers try 1 flavour each. Based on the tree diagram, what is the probability that a customer tried toffee?

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