Could you please help me to solve this question step by step? and some explanation

(7) [15 marks] There is a rare disease called Nerditosis which aiicts about 1 CS student in 1000. One symptom of Nerditosis is a compulsion to refer to everything using numbers or Greek symbols. Two professors claim that they can diagnose Nerditosis. o If the student has Nerditosis, Professor X can detect it with probability 0.99. o If the student does not Nerditosis, Professor X will erroneously detect it with probability 0.03. 0 Professor Y does not have the sophisticated equipment that Professor X has, but he knows that Nerditosis aects one in thousand students on average. Hence, when asked if a student has Nerditosis, Professor Y says \"yes\" with probability . 2 o What is the probability that Professor X misdiagnoses Nerditosis i.e. says \"yes\" when the student does not have it or ' 0\" when the student does indeed have it? [7 marks] 0 What is the probability that Professor Y misdiagnoses Nerditosis? [7 marks] 0 Which professor is more accurate in detecting Nerditosis? [1 marks]