In Township K, 1/5 of the housing units are equiped with cable Tv. If 1/10 of the housing units, including 1/3 of those that are equiped with cable tv, are equipped with videocassette recorders, what fraction of the housing units have neither cable tv nor videocassette recorders?
I calculate at the middle that 1/10*1/3= 1/30. but the answer is 1/15, why is that? I made the mistake at this point, pls instruct me. thank u~
1/5 -- cable TV (This includes some data from video cassette recorder)
1/10 -- video cassette recorder including 1/3(equiped with cable tv) i.e. 1/3(1/5) = 1/15
therefore only video cassette recorder = 1/10 - 1/15 = 1/30
Total = 1/5+1/30+neither cable tv nor videocassette recorders
1 = 7/30 + neither cable tv nor videocassette recorders
therefore neither cable tv nor videocassette recorders = 1-7/30 = 23/30