Apparently, depression significantly increases the risk of developing dementia l

Question

Apparently, depression significantly increases the risk of developing dementia later in life (BBC News, July 6, 2010). In a recent study it was reported that 22% of those who had depression went on to develop dementia, compared to only 17% of those who did not have depression. Suppose 10% of all people suffer from depression. What is the probability of a person developing dementia? (Do not round intermediate calculations. Round your answer to 3 decimal places.) Probability _______ If a person has developed dementia, what is the probability that the person suffered from depression earlier in life? (Do not round intermediate calculations. Round your answer to 3 decimal places.) Probability _______

Explanation / Answer

P(depression and dementia) = P(dementia|depression) * P(depression)         using conditional probability
P(depression and dementia) = 0.22*0.10 = 0.022
P(no depression and dementia) = P(dementia|no depression) * P(no depression) = 0.17*0.90 = 0.153

a) P(Dementia) = P(depression and dementia) + P(no depression and dementia) = 0.022 + 0.153 = 0.175

b) P(Depression | dementia) = P(Depression and dementia)/P(dementia) = 0.022/0.175 = 0.126

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.