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A college professor found herself assigned to a committee of six people composed of four men and two women​ - Alice,​ Bonnie, Carl,​ Danny, Evan, and Frank. The committee had to select two officers to carry out the majority of its administrative work.

If the officers are selected at​ random, what is the probability that both officers are​ women?

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What is the probability that at least one of the two officers is a​ woman?

Respuesta :

Answer: a) [tex]\dfrac{1}{15}[/tex]  b) [tex]\dfrac{3}{5}[/tex]

Step-by-step explanation:

Since we have given that

Number of men = 4

Number of women = 2

So, number of selected people = 2

So, the probability that both officers are women would be

[tex]\dfrac{^2C_2}{^6C_2}\\\\=\dfrac{1}{15}[/tex]

And the probability that at least one of the two officers is a woman would be

[tex]\dfrac{^2C_1\times ^4C_1}{^6C_2}+\dfrac{^2C_2}{^6C_2}\\\\=\dfrac{2\times 4}{15}+\dfrac{1}{15}\\\\=\dfrac{8}{15}+\dfrac{1}{15}\\\\=\dfrac{8+1}{15}\\\\=\dfrac{9}{15}\\\\=\dfrac{3}{5}[/tex]

Hence, a) [tex]\dfrac{1}{15}[/tex]  b) [tex]\dfrac{3}{5}[/tex]

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