Question

A group 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 vitamin0.3
0.2
0.5
Total
0.45
0.55
Select from the drop-down menus to correctly complete the statement.
Having at least one headache and taking a daily vitamin Choose...
independent events because
the probability of a patient from the group having a headache Choose...
the probability of a
patient from the group having a headache given that they take a daily vitamin
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Answer 1

Having at least one headache and taking a daily vitamin are dependent events because the probability of a patient having a headache can be influenced by whether or not they take a daily vitamin.

Step-by-step explanation:

The events of having at least one headache and taking a daily vitamin are considered dependent events because the probability of a patient having a headache can be influenced by whether or not they take a daily vitamin.

The probability of a patient from the group having a headache is 0.45. The probability of a patient from the group having a headache given that they take a daily vitamin is 0.15.

Answer 2

Having at least one headache and taking a daily vitamin are stochastically dependent events.

Step-by-step explanation:

A group 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 result.

Had at least Had no Total

one headache headache

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

Now,P(The patient takes a daily vitamin)
`*` P(The patient had at least one headache in the past week)

=
`0.5 * 0.45`

= 0.225 ≠ 0.15 = P(The patient takes a daily vitamin and had at least one headache in the past week)

Hence, having at least one headache and taking a daily vitamin are dependent events.