The data in the following table show the outcomes of the testing of an allergy drug on 500 people. $$\begin{array} { l | c | c | c | c }
& \begin{array} { c }
\text { Allergy } \
\text { drug }
\end{array} & \text { Placebo } & \begin{array} { c }
\text { Control } \
\text { (no treatment) }
\end{array} & \text { Total } \
\hline \text { Improvement } & 145 & 85 & 41 & 271 \
\text { No improvement } & 55 & 115 & 59 & 229 \
\text { Total } & 200 & 200 & 100 & 500
\end{array}$$
-What is the probability that a randomly selected person was not given the placebo or improved?
A)0.628
B)0.77
C)0.23
D)0.372

Question

The data in the following table show the outcomes of the testing of an allergy drug on 500 people. $$\begin{array} { l | c | c | c | c } 
& \begin{array} { c } 
\text { Allergy } \
\text { drug }
\end{array} & \text { Placebo } & \begin{array} { c } 
\text { Control } \
\text { (no treatment) }
\end{array} & \text { Total } \
\hline \text { Improvement } & 145 & 85 & 41 & 271 \
\text { No improvement } & 55 & 115 & 59 & 229 \
\text { Total } & 200 & 200 & 100 & 500
\end{array}$$
-What is the probability that a randomly selected person was not given the placebo or improved?
A)0.628
B)0.77
C)0.23
D)0.372

Quizplus · Accepted Answer

The probability that a person was not given the placebo or improved is calculated by adding the probability of not being given the placebo (300 out of 500) and the probability of improvement (271 out of 500), then subtracting the overlap (people who improved but were given the placebo, 85 out of 500). This gives (300 + 271 - 85) / 500 = 486 / 500 = 0.772, which rounds to 0.77.

The Data in the Following Table Show the Outcomes of the Testing