Respuesta :
Answer:
[tex](a)\dfrac{92}{117}[/tex]
[tex](b)\dfrac{8}{39}[/tex]
[tex](c)\dfrac{25}{117}[/tex]
Step-by-step explanation:
Number of Men, n(M)=24
Number of Women, n(W)=3
Total Sample, n(S)=24+3=27
Since you cannot appoint the same person twice, the probabilities are without replacement.
(a)Probability that both appointees are men.
[tex]P(MM)=\dfrac{24}{27}X \dfrac{23}{26}=\dfrac{552}{702}\\=\dfrac{92}{117}[/tex]
(b)Probability that one man and one woman are appointed.
To find the probability that one man and one woman are appointed, this could happen in two ways.
- A man is appointed first and a woman is appointed next.
- A woman is appointed first and a man is appointed next.
P(One man and one woman are appointed)[tex]=P(MW)+P(WM)[/tex]
[tex]=(\dfrac{24}{27}X \dfrac{3}{26})+(\dfrac{3}{27}X \dfrac{24}{26})\\=\dfrac{72}{702}+\dfrac{72}{702}\\=\dfrac{144}{702}\\=\dfrac{8}{39}[/tex]
(c)Probability that at least one woman is appointed.
The probability that at least one woman is appointed can occur in three ways.
- A man is appointed first and a woman is appointed next.
- A woman is appointed first and a man is appointed next.
- Two women are appointed
P(at least one woman is appointed)[tex]=P(MW)+P(WM)+P(WW)[/tex]
[tex]P(WW)=\dfrac{3}{27}X \dfrac{2}{26}=\dfrac{6}{702}[/tex]
In Part B, [tex]P(MW)+P(WM)=\frac{8}{39}[/tex]
Therefore:
[tex]P(MW)+P(WM)+P(WW)=\dfrac{8}{39}+\dfrac{6}{702}\\$P(at least one woman is appointed)=\dfrac{25}{117}[/tex]
