Hi,ishti_du!
I found the answer explanation for the question in NOVA-GRE book. Here it is:
" Since there are twice as many townhomes as ranch-style homes, the probability of selecting a
townhome is 2/3.*
Now, “there are 3 times as many townhomes with pools than without pools.” So the probability that a townhome will have a pool is 3/4.
Hence, the probability of selecting a townhome with a
pool is (2/3)x(1/4)=(1/6)
The answer is (E).
* Caution: Were you tempted to choose 1/2 for the probability because there are “twice” as many
townhomes? One-half (= 50%) would be the probability if there were an equal number of townhomes and
ranch-style homes. Remember the probability of selecting a townhome is not the ratio of townhomes to
ranch-style homes, but the ratio of townhomes to the total number of homes. To see this more clearly,
suppose there are 3 homes in the subdivision. Then 2 would be townhomes and 1 would be a ranch-style
home. So the ratio of townhomes to total homes would be 2/3. "
That's the solution the authors of the problem provided - hope it will clarify how to solve such kind of problems!
Regards,
Delyan