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 Please solve clearly

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Question: 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

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]

Please solve clearly

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