Expert: Ahmed Salami - 10/21/2008

Question
in a large locality,60% of families have a car,50% have an air conditioner and 30% have both.find the percentage of families that have
a)at least one of the items
b)neither of the two
c)have only airconditioner

Answer
Hi,
If 60% of families have a car,50% have an air conditioner and 30% have
both i.e P(a&c) = 30%
Then the percentage that has only a car,
P(c) = 60% - 30%
    = 30%
The percentage that has only air conditioner,
P(a) = 50% - 30%
    = 20%
a) And so the percentage of those who have at least one of the items,
  P(a, c, or a&c) = P(a) + P(c) + P(a&c)
                  = 20% + 30% + 30%
                  = 80%

b) The percentage of those who have neither of the two would be
  100% - 80%
= 20%

c) The percentage that has only air conditioner,
  P(a) = 50% - 30%
       = 20%
  (as above)

Regards.