Answer :
Generally, 'n' represent the sample size, 'p' is the probability of success in a single trial, and 'q' is the corresponding probability of failure in a single trial.
The given problem suggests that the randomly selected group consists of 390 subjects. It follows that the sample size considered contains 390 subjects,
[tex]n=390[/tex]The objective is to study the number of subjects who develop headaches.
So we declare here that the success for a trial is defined as a subject from the group being found to have developed headaches.
Given that 23% of the subjects given a placebo, develop headaches. So the probability that a randomly selected subject will develop headache, that is, the probability of success is given by,
[tex]\begin{gathered} p=23\text{ percent} \\ p=\frac{23}{100} \\ p=0.23 \end{gathered}[/tex]Thus, the value of 'p' is obtained as,
[tex]p=0.23[/tex]It is known that success and failure are complementary events, so the sum of their probabilities must be unity,
[tex]p+q=1[/tex]Substitute the value and solve for 'q' as follows,
[tex]\begin{gathered} 0.23+q=1 \\ q=1-0.23 \\ q=0.77 \end{gathered}[/tex]Thus, the value of 'q' is 0.77.
