Expert: Ahmed Salami - 10/20/2008

Question
74% of Martians own spaceship. 62% of the space ship owners are male and 45% of the Martians that don't own spaceships are male.  Round your percentages to 2 decimal places. (Assume only males & females)
A.  What percentage of the Martians are female?
B.  What percentage of the space ship owners are female?
C.  What percentage of the females own space ships?
D.  What percentage of the males own space ships?

Answer
Hi Sandy,
If 74% of Martians own spaceships and 62% of them are male, then the
percentage of Martians that are male and own a spaceship will be 62%
of 74% of the total population
i.e (62/100) . 74% = 45.88%
If 45% of those who dont own spaceships are male, then the percentage
of Martians that are male and dont own a spaceship will be 45% of
(100 - 74)% of the total population
i.e (45/100) . 26% = 11.7%
Therefore the percentage of male Martians is
45.88% + 11.7% = 57.58%
(since a male Martian either owns a spaceship or doesnt)

A)The percentage of Martians who are female is therefore
 (100 - 57.58)% = 42.42%

B)The percentage of the spaceship owners who are female
= (100 - 62)% i.e 38% of spaceship owners
or
38% of 74% i.e (38/100).74%
= 28.12% of the total population

C)Of the 42.42% of Martians who happen to be female, 28.12% of these
own spaceships. Therefore, the percentage of the females who own
spaceships will be
(28.12/42.42) = 66.29%
This means that 66.29% of female Martians own spaceships.

D)Of the 57.58% of Martians who happen to be male, 45.88% of these
own spaceships. Therefore, the percentage of the males who own
spaceships will be
45.88/57.58) = 79.68%
This means that 79.68% of male Martians own spaceships.

I hope its all clear.
Regards.