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)=\frac{P(A\cap B)}{P(B)}$$P(A|B)=\frac{0.06}{0.09}$$P(A|B)=0.67$