Respuesta :
Probability:
Women (W)= 130
Men (M) = 400 - 130 = 270
Total = 400
Prob(W) = 130/400 = 13/40
Prob(M) = 270/400 = 27/40
a. Probability of selecting one woman out of 3 applicants:
Possible outcomes = {WMM, MWM, or MMW}
[tex]\begin{gathered} \text{Prob(One Woman)}=\text{ (}\frac{13}{40}\times\frac{27}{39}\times\frac{26}{38})\text{ +(}\frac{27}{40}\times\frac{13}{39}\times\frac{26}{38})\text{ + (}\frac{27}{40}\times\frac{26}{39}\times\frac{13}{38})\text{ = 3 x( }\frac{27}{40}\times\frac{26}{39}\times\frac{13}{38}) \\ \\ \text{ = 0.4618 }\approx\text{ 0.46} \end{gathered}[/tex]b. Possible outcomes = {WWM, WMW, or MWW}
[tex]\begin{gathered} \text{Prob(Two Women) = (}\frac{13}{40}\times\frac{12}{39}\times\frac{27}{38})\text{ + (}\frac{13}{40}\times\frac{27}{39}\times\frac{12}{38})\text{ + (}\frac{27}{40}\times\frac{13}{39}\times\frac{12}{38})\text{ = 3(}\frac{13}{40}\times\frac{12}{39}\times\frac{27}{38}) \\ \\ \text{ = 0.213 }\approx\text{ 0.21} \end{gathered}[/tex]c. Possible outcomes = (WWW)
[tex]\text{Prob(WWW) = }\frac{13}{40}\times\frac{12}{39}\times\frac{11}{38}=0.0289\approx0.03[/tex]d.
[tex]\text{Prob(None is a woman) = 1-Prob(WWW)=1-0.0289 = 0.971}\approx0.97[/tex]The correct answers are: a. 0.46
b. 0.21
c. 0.03
d. 0.97
