Problem Bank - Probability
Access custom-built, exam-style problems for probability. Each problem has a full solution and mark-scheme, as well as AI grading and support.
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Let R be the value of a roll on 6 sided dice is shown in the following table. The probability distribution for R can be modelled by the following table.
Sally rolls the dice 100 times, and records 25 rolls of 6.
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Explain why this is not inconsistent with the table.
Josh plays a game using this dice. He pays $4 to roll the dice, and earns back the value of his roll in dollars.
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Determine the value of p and the value of q such that the game is fair.
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The masses, in grams, of chocolate bars produced by a factory can be modelled by a normal distribution with mean 100g and standard deviation 0.6g. A chocolate bar can only be packaged if its mass is greater than 99g, otherwise is it melted back into the production line.
- [2]
Find the probability that a randomly selected chocolate bar is packaged.
On a given day, the number of chocolate bars packaged is 5000.
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Estimate, to the nearest 10, the number of chocolate bars that are melted back that day.
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Given that a bar has a mass of less than 101g, find the probability it will be melted down.
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James is sitting a multiple choice exam with 15 questions. Each question has 3 answer choices, of which only one is correct.
James randomly picks an answer on each question. Let X represent the number of questions James answers correctly.
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State whether X is discrete or continuous.
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Write down the value of E(X).
Find the probability that
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X=7,
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3<X<10.
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During a very difficult practice maths quiz, 40 high‑school students each received a mark out of 100.
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Write down the median mark.
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How many students scored 24 marks or less?
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How many students scored more than 29 marks?
A passing score is 27 marks.
- [3]
Determine the probability that a student scored above 29 marks given that they passed the exam.
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