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Probability Concepts · Part 2 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.
For two events, P(A) = 0.5, P(B) = 0.3 and P(A and B) = 0.2. Find P(A or B) and P(neither A nor B).
A tramping club finds that 45% of members own a tent, 60% own a portable stove, and 25% own neither. A member is chosen at random. Find the probability the member owns both, and the probability the member owns exactly one item.
A regional airline finds that on any given flight the probability of a delay is 0.18 due to weather, 0.11 due to a technical issue, and 0.06 due to both together. A traveller has four flights on a trip. She calculates the probability of at least one delayed flight as 1 − (1 − 0.23)4 = 0.648. Evaluate her reasoning and comment on the answer.
Explain the difference between mutually exclusive events and independent events, giving an example of each.
In a town, 30% of households have a heat pump and 25% have solar panels. If these were independent, what proportion would have both? A survey finds 12% have both. Interpret this result.
An insurer models the probability that a given house in a coastal suburb suffers flood damage in a year as 0.02, and treats houses as independent. It insures 3 000 houses in the suburb and calculates that the probability of more than 100 claims in a year is negligible. Discuss the model and its consequences for the insurer.