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 25% of those who had depression went on to develop dementia, compared to only 18% of those who did not have depression. Suppose 12% of all people suffer from depression.

To 3 decimal places, what is the probability of a person developing dementia?
To 3 decimal places, if a person has developed dementia, what is the probability that the person suffered from depression earlier in life?

Explanation / Answer

A) PEOPLE SUFFERING FROM DEMENTIA WILL BE PEOPLE WHO HAVE DEPRESSION PLUS PEOPLE WHO DO NOT HAVE DEPRESSION

THEREFORE 12% SUFFER FROM DEPRESSION, 88% DO NOT HAVE DEPRESSION

NOW TOTAL DEMENTIA = 0.12*0.25+0.88*0.18= 0.188

B)12% PEOPLE HAVE DEPRESSION NOW AND ONLY 25% OF THESE SUFFER TO DEMENTIA

SO IF THE PERSON HAVE DEMENTIA SO PROBABILITY OF HIM BEEN SUFFERING FROM DEPRESSING IS 12/25=0.480

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