Question

The table shows the results of an experiment in which subjects taking either a drug or a placebo either reported fatigue or did not report fatigue.

Which calculation shows that selecting a subject who took the drug and selecting a subject who reported fatigue are dependent events?

Choose all answers that are correct.

— P(drug) = 0.6
P(drug | fatigue) ≈ 0.727
0.6 ≠ 0.727

— P(fatigue) = 0.44
P(fatigue | drug) ≈ 0.533
0.44 ≠ 0.533

— P(drug) = 0.6
P(fatigue) ≈ 0.44
0.6 ≠ 0.44

—P(drug and fatigue) = 0.32
P(drug) • P(fatigue) = 0.264
0.33 ≠ 0.264

Answer 1

Therefore, the correct options are;

-P(fatigue) = 0.44

`P(fatigue \left | \right drug)` = 0.533

--P(drug and fatigue) = 0.32

P(drug)·P(fatigue) = 0.264

Explanation:

Here we have that for dependent events,

`P(A \, and \, B)= P(A)* P(B\left | \right A )`

From the options, we have;

`P(fatigue \left | \right drug)` = 0.533

P(drug) = 0.6

P(drug and fatigue) = 0.32

Therefore

P(drug and fatigue) = P(drug)×
`P(fatigue \left | \right drug)`

= 0.6 × 0.533 = 0.3198 ≈ 0.32 = P(drug and fatigue)

Therefore, the correct options are;

-P(fatigue) = 0.44

`P(fatigue \left | \right drug)` = 0.533

--P(drug and fatigue) = 0.32

P(drug)·P(fatigue) = 0.264

Since P(fatigue) = 0.44 ∴ P(drug) = 0.264/0.44 = 0.6.