(3) Show a derivation tree for the string "ababbb" with the grammar (2 points) S AB | | A aB B Sb (4) A doctor knows that the disease meningitis causes the patient to have a stiff neck, 30% of the time. The prior probability of a patient having meningitis is 1/40,000, and the prior probability of any patient having a stiff neck is 1/ 20. S: The patient has a stiff neck. M: The patient has meningitis. What is the probability of the patient has meningitis given stiff neck condition? Show your calculation with formula. (2 points)