Answer:
The required probability is [tex]\frac{14}{33}[/tex].
Step-by-step explanation:
Probability:
The ratio of the favorable outcomes to the all possible outcomes.
Given that, 5 women and 7 men are eligible to serve on a committee.
A committee of 4 is randomly selected.
Choosing 2 women out of 5 women is
[tex]=^5C_2[/tex]
[tex]=\frac{5!}{2!(5-2)!}[/tex]
[tex]=\frac{5!}{2!3!}[/tex]
=10
Choosing 2 men out of 7 men is
[tex]=^7C_2[/tex]
[tex]=\frac{7!}{2!(7-2)!}[/tex]
[tex]=\frac{7!}{2!5!}[/tex]
=21
Total number of eligible person is = (5+7)=12
Choosing 4 member out of 12 member is
=[tex]^{12}C_4[/tex]
[tex]=\frac{12!}{4!(12-4)!}[/tex]
=495
The required probability is
[tex]=\frac{10\times 21}{495}[/tex]
[tex]=\frac{14}{33}[/tex]
