Chapter 12.3, Problem 2CYP

To determine

Tofind:the probability that test subject remained healthy given that he or she used the placebo.

Answer to Problem 2CYP

The probability that a subject stayed healthy given that he or she used the drug is $\frac{1}{4}$ .

Explanation of Solution

Given:

He or she used the placebo.

Concept used:

Probability formula:

  $\begin{array}{l}\mathrm{P}\left(\mathrm{A}\right)=\frac{\text{number of favourable events}}{\text{number of total events}}.\\ \mathrm{P}\left(\mathrm{A}\right)=\frac{\mathrm{n}\left(\mathrm{A}\right)}{\mathrm{n}},\mathrm{P}\left(\mathrm{B}\right)=\frac{\mathrm{n}\left(\mathrm{B}\right)}{\mathrm{n}}.\end{array}$

For a conditional probability the formula will be:

  $\mathrm{P}\left(\mathrm{A}|\mathrm{B}\right)=\frac{\mathrm{P}\left(\mathrm{A}\cap \mathrm{B}\right)}{\mathrm{P}\left(\mathrm{B}\right)}$ .

Calculation:

There is total of $1600+800+1200+400=4000$ .

The probability oof getting healthy from placebo user is:

  $\begin{array}{l}\mathrm{P}\left(\frac{\mathrm{H}}{\mathrm{P}\mathrm{L}}\right)=\frac{\mathrm{P}\left(\mathrm{H}\text{ and }\mathrm{P}\mathrm{L}\right)}{\mathrm{P}\left(\mathrm{P}\mathrm{L}\right)}.\\ \Rightarrow \frac{400}{4000}÷\frac{1600}{4000}.\\ \Rightarrow \frac{1}{10}\times \frac{40}{16}.\\ \Rightarrow \frac{1}{4}.\end{array}$

Hence, the probability that a subject stayed healthy given that he or she used the drug is $\frac{1}{4}$ .