Answer:
(a) The probability of an adult using non-prescription antidepressants given that he visited the therapist is 0.78.
(b) The probability of an adult visited the therapist given that he was using non-prescription antidepressants is 0.46.
Step-by-step explanation:
Conditional probability of an event X given that another event Y has already occurred is:
[tex]P(X|Y)=\frac{P(X\cap Y)}{P(Y)}[/tex]
Let A = an adult visited the therapist and B = an used non-prescription antidepressants.
Given:
P (A) = 0.27
P (B) = 0.46
P (A ∩ B) = 0.21
(a)
Compute the probability that a randomly selected adult who visited a therapist during the past year also used non-prescription antidepressants as follows:
[tex]P(B|A)=\frac{P(A\cap B)}{P(A)} =\frac{0.21}{0.27} =0.77778\approx0.78[/tex]
Thus, the probability of an adult using non-prescription antidepressants given that he visited the therapist is 0.78.
(b)
Compute the probability that a randomly selected adult visited a therapist during the past year, given that he or she used non-prescription antidepressants as follows:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)} =\frac{0.21}{0.46} =0.4565\approx0.46[/tex]
Thus, the probability of an adult visited the therapist given that he was using non-prescription antidepressants is 0.46.
