question from 2010 exam

[ammor]

Hi David,

can you please provide a clear answer about this question?

40% of the total auto owners will go for auto insurance, 60% of total home only owners will go for home insurance, 80% of both auto and home owners will go for both auto and home insurance. It is given that at least 65% of the people were auto owners and 50% were home owners and 15% have both home and auto. find the prob. for people who would go for atleast one insuance.

 

[Jiew Kwang]

gosh. this qn is a headache..

 

[David Harper CFA FRM]

Hi ammor,

I guess this question was on the May exam?
see http://forum.bionicturtle.com/viewreply/6118/
... yikes, i don't understand why really, it's not Bayes i don't think ....

I can't do better than Roman:
"i agree with the suggested result. 53% should be good.
(0.65 - 0.15) x 0.40 + (0.50 - 0.15) x 0.60 + 0.15 x 0.80 = 0.53"

this presumes the population divides into:
50% auto only
15% auto & home; i.e., the "overlap" in a Venn (65% Auto, 50% Home)
35% home only

although frankly I'm not totally satisfied: "80% of both auto and home owners will go for both auto and home insurance" does not imply that 80% of both A&H will go for EITHER auto & home, which is all we need for the 15% segment (??) ... some of GARP's questions I don't try to hard on because it's not necessarily a well-crafted question (I could be wrong, maybe i miss something)

David