(C) the mayor for just one of the three years after 2004 belongs to the Blue Party. [3] (iii) Find the conditional probability that the mayor in 2005 belongs to the Red Party, given that the mayor in 2007 belongs to the Red Party. [3] 4. Newborn babies are tested for a mild illness which affects 1 in 500 babies. The result of a test is either positive or negative. A positive test suggests the baby has the illness. However, the test is not perfect: o for babies with the illness, the probability of a positive result is 0.99 o for babies without the illness, the probability of a negative result is 0.95 (i) Copy and complete this probability tree diagram to illustrate the situation. Positive H\" me result 0.002 illness N \"v: 5.53. [2] (ii) Find the probability that (A) the result is positive, [3] (B) the test gives the correct diagnosis. [2] (iii) Given that the result of a test is positive, show that the conditional probability that the baby has the illness is 0.038 (correct to 3 decimal places). Comment on the test in the light of this value being so low. [4] It is required to raise the probability found in part (iii) by improving the testing process. To achieve this, it is intended to increase the probability of negative results for babies who do not have the illness from its current value of 0.95 to p. (iv) Find the value of p that would raise the probability in part (iii) to 0.5. [4]