****URGENT******
1A)Â Â An event has four possible outcomes, A, B, C, andD. All of the outcomes are disjoint.
Given that P(Bc) = 0.2, P(A) = 0.1,and P(C) = 0.3, what is P(D)?
1B) A study was conducted on a potential association betweendrinking coffee and being diagnosed with clinical depression. All18,832 subjects were female. The women were free of depression atthe start of the study in 1996. Information was collected on coffeeconsumption and the incidence of clinical depression during theten-year study period.
| ≤ 1 cup coffee per week | 2-6 cups coffee per week | TOTALS |
Diagnosis of clinical depression | 670 | 373 | 1043 |
No diagnosis of clinical depression | 11,545 | 6244 | 17789 |
TOTALS | 12,215 | 6,617 | 18,832 |
Are the following events independent?
Event LC: The event of drinking less than or equal to 1 cup ofcoffee per week
(Little Coffee = LC)
Event D: The event of a diagnosis of clinical depression
(Depression = D)
Round your calculations to four decimal places (orfewer) at each step.
There are multiple ways to test for independence. All involvethe comparison of observed and expected probabilities based onprobability theory.
In this context:
If the two probabilities are similar (identical to two decimalplaces), this is evidence of independence.
If the two probabilities are not similar (not identical to twodecimal places), this is evidence of a lack of independence.
C) What do your results in (b) tell us, about the ways in whichdrinking very little coffee (0-1 cups per week) influences, or doesnot influence, the probability of depression for women in the studypopulation?
