AQA GCSE · Question 16.2 · Statistical Measures and Calculations
At £150 000, what is the risk that she will not sell her house within two months?
How to approach this question
This is a question about combined probability. You know the risk of not selling in any single month from the previous question. To find the risk of not selling for two consecutive months, you need to combine these probabilities. Remember the "and" rule for independent events: P(A and B) = P(A) * P(B).
Full Answer
The risk of not selling in one month is 0.75.
Assuming the events are independent, the risk of not selling in the first month AND not selling in the second month is:
Risk = 0.75 * 0.75 = 0.5625.
From the previous part, the risk (probability) of not selling the house in any given month at the price of £150,000 is 0.75.
We want to find the probability of not selling in the first month AND not selling in the second month.
We assume that the event of not selling in the first month is independent of the event of not selling in the second month.
For independent events, the probability of both occurring is the product of their individual probabilities.
P(not selling in 2 months) = P(not selling in month 1) × P(not selling in month 2)
P(not selling in 2 months) = 0.75 × 0.75
P(not selling in 2 months) = 0.5625.
The risk is 0.5625 (or 56.25%).
Common mistakes
✗ Adding the probabilities (0.75 + 0.75) instead of multiplying.
✗ Calculating the probability of selling (1 - 0.5625) instead of not selling.
✗ Using an incorrect value from the previous part.
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