We can solve this using Bayes formula:
P(B|A) = P(A|B)·P(B) / P(A)
Assume A refer to stiff neck and B refer to probability of meningitis,
P(A|B) = meningitis causes stiff neck =50%= 0.5
P(A)=1/20
P(B)= 1/50000
P(B|A) = 0.5*1/50000/(1/20)= 0.02%
Answer is B