Apparently depression significantly increases the risk of de

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?

Solution

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