## Precalculus (6th Edition) Blitzer

The probability that a randomly picked American has done 4 years of high school only or is a woman is $\frac{39}{58}$.
We know that the probability that a randomly picked American has done 4 years of high school only or is a woman: \begin{align} & P\left( \text{completed 4 years of high school} \right)=\frac{(\text{Numbers of students completed 4 years of high school)}}{(\text{Total numbers of students)}} \\ & =\frac{56}{174} \\ & P\left( \text{women} \right)=\frac{(\text{Total numbers of women)}}{(\text{Total numbers of students)}} \\ & =\frac{92}{174} \end{align} \begin{align} & P\left( \text{4 years of high school only and a woman} \right)=\frac{(\text{Total numbers women of high school only)}}{(\text{Total numbers of students)}} \\ & =\frac{31}{174} \end{align} \begin{align} & P\left( \text{4 years of high school or is a woman} \right)=\left[ P\left( \text{4 years of high school only} \right)+P\left( \text{woman} \right)-P\left( \text{4 years of high school only and a woman} \right) \right] \\ & =\frac{56}{\text{174}}+\frac{92}{\text{174}}-\frac{31}{174} \\ & =\frac{117}{174} \\ & =\frac{39}{58} \end{align} Hence, the probability that a randomly picked American has done 4 years of high school only or is a woman is $\frac{39}{58}$.