Answer :
We will answer the question a) using the following formula:
[tex]P(N|T)=\frac{P(N\cap T)}{P(T)}[/tex]where we have the following event:
[tex]\begin{gathered} N=\text{ Adult use non-prescription antidepressants} \\ T=Adult\text{ visit a therapist} \end{gathered}[/tex]Therefore, the probability P(N|T) is the probability of a randomly selected adult use non-prescription antidepressants given that he visited the therapist. This formula is known as conditional probability formula.
To use the formula, we have to calculate the probability :
[tex]P(N\text{ }\cap T)[/tex]This is the probability of the intersection between the events N and T, that is, the probability that a given adult visits a therapist and use non-prescription antidepressants. Thsi information was given in the question, so we have
[tex]P(N\cap T)=21\%=0.21[/tex]Therefore, we can calculate the probability required in the part a) as :
[tex]P(N|T)=\frac{P(N\cap T)}{P(T)}=\frac{21\%\text{ }}{26\%}=\frac{0.21}{0.26}\approx0.81=81\%\text{ }[/tex]Therefore, the answer for the part a) is 81%, or in decimal number 0.81.
Part b)
We are asked to calculate the probability of that a randomly selected patient who use non-prescription antidepressants visit the therapist. This can be written in symbols as (we use the notations from the solution of the part a))
[tex]P(T|N)=\frac{P(T\cap N)}{P(N)}=\frac{21\%}{43\%}=\frac{0.21}{0.43}\approx0.49=49\%\text{ }[/tex]Therefore, the answer for the part b) is 49%, or in decimal number 0.49.