The table below gives details of symptoms of patients and whether or not they were suffering from meningitis.

ID	Headache	Fever	Vomiting	Meningitis
1	true	true	false	False
2	false	true	false	False
3	true	false	true	False
4	true	false	true	False
5	false	true	false	True
6	true	false	true	False
7	true	false	true	False
8	true	false	true	True
9	false	true	false	False
10	true	false	true	True

Using this dataset calculate the following probabilities: a. P(Vomiting = true). b. P(Headache = true, Vomiting = false). C. P (Vomiting = false | Headache = true) d. P(Meningitis | Fever = true, Vomiting = false)