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15 exam-style questions with model answers, plus 15 quick multi-choice questions — every question on the site for this standard, grouped by the 5 pages of notes they come from.
Write a full answer before you reveal the model one — that comparison is where the marks come from. Every block links back to the notes that teach it.
Using the table (100 students), find the probability that a randomly chosen student passed.
Using the table, find the probability that a student failed, given that they did not study.
A student claims: 'Studying makes no difference to whether you pass.' Using the table, evaluate this claim.
Out of 80 cyclists, 20 were injured in a year. Find the risk of injury for a cyclist.
The risk of a fault is 0.08 for machine A and 0.02 for machine B. Find the relative risk of a fault for machine A compared with machine B, and interpret it.
A report says: 'People who skip breakfast have a relative risk of 1.5 for being late to work.' A manager concludes that skipping breakfast causes lateness. Evaluate this conclusion.
A fair coin is tossed twice. Find the probability of two heads.
A bag has 5 green and 3 yellow sweets. Two are taken without replacement. Find the probability that both are green.
A bag has 4 red and 6 blue counters. Two are drawn without replacement. Find the probability of getting at least one red.
A normal distribution has mean 50 and standard deviation 10. Find the z-score of the value 65.
Test scores are normally distributed with mean 60 and standard deviation 12. Find the probability that a randomly chosen score is less than 78.
The weights of bags of flour are normally distributed with mean 1000 g and standard deviation 15 g. The heaviest 5% are set aside. Find the minimum weight for a bag to be set aside.
A spinner is spun 50 times and lands on red 20 times. Find the experimental probability of red.
A coin is tossed 40 times and shows heads 24 times. Compare the experimental probability of heads with the theoretical value.
Explain how you could use random digits (0–9) to simulate whether each of 5 buses is on time, given that a bus is on time 70% of the time, and describe how to estimate the probability that all 5 are on time.