Data Science with Rationale One multiple Choice Question

Conditional probability
The text and table below are from OpenIntro Stats. Use the table to calculate P(lived | inoculated)
for the given sample and explain your answer.
a
The smallpox data set provides a sample of 6,224 individuals from the year 1721 who were
exposed to smallpox in Boston. Doctors at the time believed that inoculation, which involves
exposing a person to the disease in a controlled form, could reduce the likelihood of death.
Each case represents one person with two variables: inoculated and result. The variable
inoculated takes two levels: yes or no, indicating whether the person was inoculated or not. The
variable result has outcomes lived or died. These data are summarized in Tables 3.15 and 3.16.
inoculated
no
result
lived
died
Total
yes
238
6
244
5136
844
5980
Total
5374
850
6224
Figure 3.15: Contingency table for the smallpox data set.
O A. 238/5374 = 0.044
B. 238/6224 = 0.038
O C. 238/244 = 0.975
D. 5374/6244= 0.845
O E. 5736/5980 = 0.858
Rationale*