#### Answer

a. $0.192$
b. $0.269$
c. $0.538$
d. $0.013$

#### Work Step by Step

The total number of outcomes is $_{13}C_2=78$
a. The probability that both are filled by men.
Favorable outcomes for this case is $_6C_2=15$ and
The probability is $p1=15/78=0.1923$
b. The probability that both are filled by women.
Favorable outcomes for this case is $_7C_2=21$ and
The probability is $p2=21/78=0.2692$
c. The probability that one man and one woman are hired.
Favorable outcomes for this case is $_6C_1\times_7C_1=42$ and
The probability is $p3=42/78=0.53846$
d. The probability that the one man and one woman who are twins are hired.
Favorable outcomes for this case is $1$ and
The probability is $p4=1/78=0.0128$