What are the answers to Question 2?

Question 2 [4 marks]

You know the following statistics about fire:

• The probability of your house catching fire on any particular day is 1 in 10,000
• Your fire alarm correctly detects a house fire 95% of the time
• The probability that your fire alarm sounds on a day when there is no fire (a false alarm) is 1 in 100.

a) Your alarm goes off. What is the probability that your house is on fire? [1 mark]

b) Many people given this problem estimate the probability of the house being on fire as close to 95%. Provide one possible explanation for this error. [1 mark]

c) Express and solve this problem using natural frequencies. [2 marks]