it is estimated that 93% of senior citizens suffer from sleep disorders and 7% 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 a sleep disorder. round your answer to the nearest hundredth.

(b) 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.

Question

it is estimated that 93% of senior citizens suffer from sleep disorders and 7% 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 a sleep disorder. round your answer to the nearest hundredth.

(b) 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.

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Conditional Probability" ], "new_concepts": [], "current_concepts": [ "Conditional Probability" ] } ## Define given probabilities $$ \begin{aligned} P(S) &= 0.93 \ P(A) &= 0.07 \ P(S \cap A) &= 0.06 \end{aligned} $$ ## Calculate conditional probability for part (a) $$ \begin{aligned} P(A \mid S) &= \frac{P(A \cap S)}{P(S)} \ P(A \mid S) &= \frac{0.06}{0.93} \approx 0.0645 \approx 0.06 \end{aligned} $$ ## Calculate conditional probability for part (b) $$ \begin{aligned} P(S \mid A) &= \frac{P(S \cap A)}{P(A)} \ P(S \mid A) &= \frac{0.06}{0.07} \approx 0.8571 \approx 0.86 \end{aligned} $$ ## Question 1 (a) 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. 0.06 ## Question 2 (b) 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. 0.86 { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Statistics", "Conditional Probability" ] }

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QUESTION IMAGE

Question

Explanation:

Define given probabilities

Calculate conditional probability for part (a)

Calculate conditional probability for part (b)

Answer:

Question 1

Question 2