(1) Imagine that 5% of the cobras in India develop a genetic mutation that makes their venom especially dangerous to mongooses. Suppose that normal cobras have a 25% chance of winning a battle with a mongoose but cobras with the mutation have a 90% chance of winning a battle with a mongoose. On a wildlife viewing holiday in India, you witness a battle between a cobra and a mongoose. (Assume the cobra is selected uniformly at random from all of the cobras in India.) (i) What is the probability that the cobra has the mutation given that it wins the battle? (ii) What is the probability that the cobra has the mutation given that it wins the battle and immediately afterwards it loses a battle with another mongoose? (Assume the outcomes of the two battles are independent.) N [Fully explain your answer for (i). Brief explanation required for (ii).]