Question

It is estimated that 89% of senior citizens suffer from sleep disorders and 9% suffer from anxiety. Moreover, 6% of senior citizens suffer from both sleep disorders and anxiety.

(a) Find the probability that a senior citizen suffers from anxiety, given that he or she has sleep disorder. Round your answer to decimal places.
(b) Given that a senior citizen suffers from anxiety, what is the probability that he or she also suffers from sleep disorder? Round your answer to decimal places.

Answer 1

a) 6.74% b) 66.7%

Explanation:

To solve it, the conditional probability is used. It establish that the probability (P) of occurrence of an event A given an event B is

P (A/B) = P (A and B) / P (B)

Let be

SD = senior citizens suffer from sleep disorders

AX = senior citizens suffer from anxiety

The the probabilities are

P (SD) = 0.89

P (AX) = 0.09

P (SD and AX) = 0.06

According to the formula, the probability that a senior citizen suffers from anxiety, given that he or she has sleep disorder is

P(AX/SD) = P (SD and AX) / P (SD)

P(AX/SD) = 0.06 / 0.89 = 0.0674 = 6.74%

According to the formula, the probability that a senior citizen suffers from sleep disorder, given that he or she has anxiety is

P(SD/AX) = P (SD and AX) / P (AX)

P(SD/AX) = 0.06 / 0.09 = .066 = 66.6%