probability that this sfudent is à mle? Pinid The cosdngp that this student is a
ID: 3364089 • Letter: P
Question
probability that this sfudent is à mle? Pinid The cosdngp that this student is a female. 9. 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 al people suffer from depression. a. What is the probability of a person developing dementia? b. If a person has developed dementia, what is the probability that the person suffered from depression earlier in life?Explanation / Answer
P(Dem|Dep) = 0.22
P(Dem|Dep') = 0.17
P(Dep) = 0.1
a)
P(Dem) = P(Dem|Dep)*P(Dep) + P(Dem|Dep')*P(Dep')
P(Dem) = 0.22*0.1 + 0.17*0.9
P(Dem) = 0.175
b)
P(Dep|Dem) = P(Dem|Dep)*P(Dep) / P(Dem)
= 0.22*0.1 / 0.175
= 0.1257
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