Answer
$P(both~are~women)=\frac{2}{7}\approx0.286$
Work Step by Step
The sample space = {man 1, man 2, man 3, woman 1, woman 2, woman 3, woman 4}. So, N(S) = 7, N(woman) = 4 and N(man) = 3.
A person is randomly selected:
$P(1st~person~is~a~woman)=\frac{N(woman)}{N(S)}=\frac{4}{7}.$
Now, there are six remaining people.
The new sample space = {man 1, man 2, man 3, woman 1, woman 2, woman 3}. So, N(S) = 6, N(woman) = 3 and N(man) = 3.
Now, a second person is randomly selected:
$P(2nd~person~is~a~woman~|~1st~person~is~a~woman)=\frac{N(woman)}{N(S)}=\frac{3}{6}=\frac{1}{2}.$
Using the General Multiplication Rule (see page 289):
$P(both~are~women)=P(1st~person~is~a~woman)\times P(2nd~person~is~a~woman~|~1st~person~is~a~woman)=\frac{4}{7}\times\frac{1}{2}=\frac{2}{7}\approx0.286.$
