(a) (b) It is estimated that % of senior citizens suffer from sleep disorders an
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Question
(a)
(b)
It is estimated that % of senior citizens suffer from sleep disorders and % suffer from anxiety. Moreover, % of senior citizens suffer from both sleep disorders and anxiety. (a) 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.(b) Find the probability that a senior citizen suffers from anxiety, given that he or she has sleep disorder. Round your answer to decimal places.
(If necessary, consult a list of formulas.)Explanation / Answer
When two events, A and B, are independent, the probability of both occurring is P (A and B) =P (A) * P (B)
The probability that a senior citizen suffers from sleep disorder is 0.9. The probability that a senior citizen suffers from anxiety is 0.09 and the probability that a senior citizen suffers from both sleep disorder and anxiety is 0.06.
When two events, A and B, are independent, the probability of both occurring is P (A and B) =P (A) * P (B)
The probability that a senior citizen suffers from sleep disorder is 0.9. The probability that a senior citizen suffers from anxiety is 0.09 and the probability that a senior citizen suffers from both sleep disorder and anxiety is 0.06.
- Given that a senior citizen suffers from anxiety, then the probability that he or she also suffers from sleep disorder is 0.09* 0.06 = 0.0054. This cannot be rounded off to 2 decimal places as the first two places after the decimal are 0.
- The probability that a senior citizen suffers from anxiety, given that he or she has sleep disorder is 0.9* 0.06 = 0.054 = 0.05 on rounding off to 2 decimal places.
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