It is estimated that 88% of senior citizens suffer from steep disorders and 7% suffer from anxiety. Moreover, 5% of senior citizens suffer from both sleep disorders and anxiety. Find the probability that a senior citizen suffers from anxiety, given that he or she has sleep disorder. Round your answer to 2 decimal places.

Given:

- \( P(S) = 0.88 \) (Probability that a senior citizen suffers from sleep disorders)
- \( P(A) = 0.07 \) (Probability that a senior citizen suffers from anxiety)
- \( P(S \cap A) = 0.05 \) (Probability that a senior citizen suffers from both sleep disorders and anxiety)

We need to find the conditional probability that a senior citizen suffers from anxiety, given that he or she has a sleep disorder, denoted by \( P(A|S) \).

The formula for conditional probability is:

\[
P(A|S) = \frac{P(S \cap A)}{P(S)}
\]

Substituting the given values:

\[
P(A|S) = \frac{0.05}{0.88} \approx 0.0568
\]

Rounding to two decimal places:

\[
P(A|S) \approx 0.06
\]

So, the probability that a senior citizen suffers from anxiety, given that he or she has a sleep disorder, is approximately **0.06** (rounded to two decimal places).

Would you like more details on this calculation or have any other questions?

Here are 8 related questions you might find useful:

1. How do you calculate the probability of the union of two events?
2. What is the importance of rounding in probability calculations?
3. Can you explain the difference between independent and dependent events?
4. How would this scenario change if the conditions were independent?
5. What is Bayes' theorem, and how does it relate to conditional probability?
6. How does conditional probability affect decision-making in healthcare?
7. What if the joint probability was different—how would that affect the conditional probability?
8. How can Venn diagrams help in understanding conditional probabilities?

**Tip:** When rounding probabilities, it's important to consider the context and significance of the precision to avoid misleading interpretations.

Calculate the probability that a senior citizen suffers from anxiety, given that he or she has a sleep disorder. Includes step-by-step solution using conditional probability formula. Key data 88% suffer from sleep disorders, 7% suffer from anxiety, and 5% suffer from both.

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