Agroup of patients were asked whether they take a daily vitamin and whether they had at least one headache in the past week.

the table shows the probabilities of results. had at least one headache

had no headaches total

takes a daily vitamin 0.15 0.35 0.5

does not take a daily vitamin 0.3 0.2 0.5

total 0.45 0.55 1

select from the drop-down menus to correctly complete the statement. having at least one headache and taking a daily vitamin independent events because the probability of a patient from the group having a headache the probability of a patient from the group having a headache given that they take a daily vitamin.