Answer: [tex]\dfrac{34}{55}[/tex]
Step-by-step explanation:
Given : The board of directors of Saner Automatic Door Company consists of 12 members, 3 of whom are women.
Number of Men = 12-3=9
Now, the probability that at least 1 member of the committee is a woman= 1- Probability all members are men. (1)
Number of combinations of choosing all men members = [tex]^9C_3[/tex]
[tex]=\dfrac{9!}{3!(9-3)!}=84[/tex]
Number of combinations of choosing any 3 members out of 12
=[tex]^{12}C_3=\dfrac{12!}{3!(12-3)!}=220[/tex]
Probability that all members of the committee are men=[tex]\dfrac{84}{220}[/tex]
Now, from (1)
The probability that at least 1 member of the committee is a woman will be
[tex]=1-\dfrac{84}{220}\\\\=\dfrac{220-84}{220}\\\\=\dfrac{136}{220}\\\\=\dfrac{34}{55}[/tex]
Hence, the probability that at least 1 member of the committee is a woman= [tex]\dfrac{34}{55}[/tex]
