Question

It is estimated that, during the past year, 27% of all adults visited a therapist and 46% of all adults used non-prescription antidepressants. It is also estimated that 21% of all adults both visited a therapist and used a non-prescription antidepressant during the past year.
(a) What is the probability that a randomly selected adult who visited a therapist during the past year also used non-prescription antidepressants? Round your answer to 2 decimal places.

(b) What is the probability that an adult visited a therapist during the past year, given that he or she used non-prescription antidepressants? Round your answer to 2 decimal places.

Answer 1

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:

$P(X|Y)=\frac{P(X\cap Y)}{P(Y)}$

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:

$P(B|A)=\frac{P(A\cap B)}{P(A)} =\frac{0.21}{0.27} =0.77778\approx0.78$

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:

$P(A|B)=\frac{P(A\cap B)}{P(B)} =\frac{0.21}{0.46} =0.4565\approx0.46$

Thus, the probability of an adult visited the therapist given that he was using non-prescription antidepressants is 0.46.