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Probability Concepts · Part 1 of 4
6 exam-style questions with model answers, plus 8 quick multi-choice questions — every question on this part of the standard, grouped by the 2 pages of notes they come from.
Write a full answer before you reveal the model one. That comparison is where the learning happens.
A six-sided die is rolled 300 times and shows a six on 58 occasions. State the model estimate and the experimental estimate of the probability of rolling a six.
A manufacturer's model predicts that 2% of its components are defective. In a sample of 4 000 components, 118 are defective. Compare the two estimates and explain what could account for the difference.
A conservation group models the probability that a monitored kākā nest fledges at least one chick as 0.35, assuming nests fail independently of one another. Over one season, 8 of 40 monitored nests fledged a chick (0.20). The group concludes the model is wrong and revises the probability to 0.20. Discuss.
Define what it means for a process to be random, and explain why a run of six heads in a row does not mean a coin is unfair.
A lottery player notes that the number 17 has not been drawn in the last 40 draws and buys a ticket with 17 on it, saying it is 'overdue'. Explain the error, and explain why the law of large numbers does not support the player's reasoning.
A regional health service notices that a rare childhood illness, which affects about 1 child in 20 000 per year nationally, has affected 3 children in one small town of 4 000 people within 18 months. Residents demand an investigation into a local cause. Discuss what probability theory says about this cluster and how the health service should respond.