Question

It is estimated that 88% of senior citizens suffer from sleep disorders and 7% suffer from anxiety. Moreover, 5% 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 a sleep disorder? Round your answer to the nearest hundredth. B) Find the probability that a senior citizen suffers from anxiety, given that he or she has a sleep disorder. Round your answer to the nearest hundredth.

Answer 1

Answer:

a) 0.71

b) 0.06

Step-by-step explanation:

We solve using Baye's Theorem

It is estimated that 88% of senior citizens suffer from sleep disorders and 7% suffer from anxiety. Moreover, 5% of senior citizens suffer from both sleep disorders and anxiety.

We have Two events

A and B

Events A = 88% of senior citizens suffer from sleep disorders

P(A) = 0.88

Event B = 7% suffer from anxiety

P(B) = 0.07

Moreover, 5% of senior citizens suffer from both sleep disorders and anxiety.

P(A and B) = 0.05

a)Given that a senior citizen suffers from anxiety, what is the probability that he or she also suffers from a sleep disorder? Round your answer to the nearest hundredth.

This is calculated as:

P(A and B)/P(B)

= 0.05/0.07

= 0.7142857143

Approximately = 0.71

B) Find the probability that a senior citizen suffers from anxiety, given that he or she has a sleep disorder. Round your answer to the nearest hundredth.

This is calculated as:

P(A and B)/P(A)

= 0.05/0.88

= 0.0568181818

Approximately = 0.06