Answer: 0.08
Step-by-step explanation:
Given : The probability that the person is female : P(F)=80%=0.080
The probability that the females attended college : P(A|F)=90%=0.90
Then, the probability that the females do not attended college :
![P(A^c|F)=1-P(A|F)=1-0.90=0.10](https://tex.z-dn.net/?f=P%28A%5Ec%7CF%29%3D1-P%28A%7CF%29%3D1-0.90%3D0.10)
Now using conditional probability formula :
![P(M|N)=\dfrac{P(M\cap N)}{P(N)}](https://tex.z-dn.net/?f=P%28M%7CN%29%3D%5Cdfrac%7BP%28M%5Ccap%20N%29%7D%7BP%28N%29%7D)
We get,
![P(A^c|F)=\dfrac{P(A^c\cap F)}{P(F)}](https://tex.z-dn.net/?f=P%28A%5Ec%7CF%29%3D%5Cdfrac%7BP%28A%5Ec%5Ccap%20F%29%7D%7BP%28F%29%7D)
Substitute the values , we get
![0.10=\dfrac{P(A^c\cap F)}{0.80}\\\\\Rightarrow\ P(A^c\cap F)=0.80\times0.10=0.08](https://tex.z-dn.net/?f=0.10%3D%5Cdfrac%7BP%28A%5Ec%5Ccap%20F%29%7D%7B0.80%7D%5C%5C%5C%5C%5CRightarrow%5C%20P%28A%5Ec%5Ccap%20F%29%3D0.80%5Ctimes0.10%3D0.08)
Hence, the probability that the person selected is a female who did NOT attend college is 0.08 .