Question

It is estimated that 91% of senior citizens suffer from sleep disorders and 9% suffer from anxiety. Moreover, 6% of seniors sufferfrom both sleep disorders and anxiety (a) Find the probability that a senior citizen suffers from anxiety, given that he or she has asleep disorder. Round your answer to the nearest hundredth.(b) Given that a senior citizen suffers from anxiety, what is the probability that he or shealso suffers from a sleep disorder? Round your answer to the nearest hundredth.

Answer 1

The probability of senior citizens suffer from sleep disorders is

`P(A)=0.91`

The probability of senior citizens suffer from anxiety is,0.09.

`P(B)=0.09`

The probability of seniors suffer from both sleep disorders and anxiety is,

`P(A\cap B)=0.06`

a. The probability that a senior citizen suffers from anxiety, given that he or she has a

sleep disorder.

`P(A|B)=(P(A\cap B))/(P(B))`
`P(A|B)=(0.06)/(0.09)`
`P(A|B)=0.67`