Answer:
![(a)\dfrac{92}{117}](https://tex.z-dn.net/?f=%28a%29%5Cdfrac%7B92%7D%7B117%7D)
![(b)\dfrac{8}{39}](https://tex.z-dn.net/?f=%28b%29%5Cdfrac%7B8%7D%7B39%7D)
![(c)\dfrac{25}{117}](https://tex.z-dn.net/?f=%28c%29%5Cdfrac%7B25%7D%7B117%7D)
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 <u>without replacement.</u>
(a)Probability that both appointees are men.
![P(MM)=\dfrac{24}{27}X \dfrac{23}{26}=\dfrac{552}{702}\\=\dfrac{92}{117}](https://tex.z-dn.net/?f=P%28MM%29%3D%5Cdfrac%7B24%7D%7B27%7DX%20%5Cdfrac%7B23%7D%7B26%7D%3D%5Cdfrac%7B552%7D%7B702%7D%5C%5C%3D%5Cdfrac%7B92%7D%7B117%7D)
(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)![=P(MW)+P(WM)](https://tex.z-dn.net/?f=%3DP%28MW%29%2BP%28WM%29)
![=(\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}](https://tex.z-dn.net/?f=%3D%28%5Cdfrac%7B24%7D%7B27%7DX%20%5Cdfrac%7B3%7D%7B26%7D%29%2B%28%5Cdfrac%7B3%7D%7B27%7DX%20%5Cdfrac%7B24%7D%7B26%7D%29%5C%5C%3D%5Cdfrac%7B72%7D%7B702%7D%2B%5Cdfrac%7B72%7D%7B702%7D%5C%5C%3D%5Cdfrac%7B144%7D%7B702%7D%5C%5C%3D%5Cdfrac%7B8%7D%7B39%7D)
(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)![=P(MW)+P(WM)+P(WW)](https://tex.z-dn.net/?f=%3DP%28MW%29%2BP%28WM%29%2BP%28WW%29)
![P(WW)=\dfrac{3}{27}X \dfrac{2}{26}=\dfrac{6}{702}](https://tex.z-dn.net/?f=P%28WW%29%3D%5Cdfrac%7B3%7D%7B27%7DX%20%5Cdfrac%7B2%7D%7B26%7D%3D%5Cdfrac%7B6%7D%7B702%7D)
In Part B, ![P(MW)+P(WM)=\frac{8}{39}](https://tex.z-dn.net/?f=P%28MW%29%2BP%28WM%29%3D%5Cfrac%7B8%7D%7B39%7D)
Therefore:
![P(MW)+P(WM)+P(WW)=\dfrac{8}{39}+\dfrac{6}{702}\\$P(at least one woman is appointed)=\dfrac{25}{117}](https://tex.z-dn.net/?f=P%28MW%29%2BP%28WM%29%2BP%28WW%29%3D%5Cdfrac%7B8%7D%7B39%7D%2B%5Cdfrac%7B6%7D%7B702%7D%5C%5C%24P%28at%20least%20one%20woman%20is%20appointed%29%3D%5Cdfrac%7B25%7D%7B117%7D)
Wait i’m confused on how this equation is modeled i’m sorry do you have a picture? i wanna be sure i answer this right.
= ( x + 2 )°
= (7y)°
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