Question

It is estimated that 92% of senior citizens suffer from sleep disorders and 8% 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 2decimal 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 2 decimal places.

Answer 1

Given,

P(Sleep disorder) = 0.92, P(Anxiety) = 0.08

P( Sleep disorder AND Anxiety) = 0.06

a)

We have to calculate P( Anxiety | Sleep disorder) = ?

Using conditional formula,

P( A | B) = P( A AND B) / P(B)

So,

P( Anxiety | Sleep disorder) = P( Anxiety AND Sleep disorder) / P( Sleep disorder)

= 0.06 / 0.92

= 0.07 (rounded to two decimale places)

b)

P( Sleep disorder | Anxiety) = ?

P( Sleep disorder | Anxiety ) =P( Anxiety And Sleep disorder) / P( Anxiety)

= 0.06 / 0.08

= 0.75