A test for breast cancer correctly classifies 95% of malignant tumours as malignant but also incorrectly classifies 1% of benign tumours as malignant. It is thought that approximately 5% of samples submitted for this test are taken from malignant tumours.
a) What are the false positive and false negative rates?
b) What is the probability that a tumour classified by this test as malignant is in
fact malignant?
i) Solve this problem by drawing up a contingency table, AND
ii) Solve using conditional probability and the law of total probability.