The probability that a person gets a certain disease is 0.15. If a person gets the disease, the probability that a doctor will give a correct diagnosis is 0.97. If a person does not get the disease, the corresponding probability is 0.88. If a computer is used instead of the doctor, the probability of giving a correct diagnosis is 0.95 whether the person gets the disease or not. (12 marks)

(a)Find the probability that the doctor will give a correct diagnosis and the

probability that the computer will give a correct diagnosis.

Comparing the doctor and the computer, which one is more likely to give a correct diagnosis?

(b)Find the probability that the doctor diagnoses that

(i)a person gets the disease (a 'positive' diagnosis)

(ii)a person does not get the disease (a 'negative' diagnosis).

What are the corresponding probabilities for the computer?

(c)Given that the doctor gives a 'positive' diagnosis, find the probability

(i)that the person gets the disease,

(ii)that the person does not get the disease.

(d)The most serious cause for concern is when a 'negative' diagnosis is given when the person really gets the disease. Comparing the doctor and the computer only on the probability of this happening, which one gives a more accurate diagnosis?