# Chapter 10 - Review Exercises - Page 1126: 86

The probability that a randomly selected student attends a private college or is from a high-income family is $\frac{12}{35}$.

#### Work Step by Step

We know that the probability that a student attends a private college is: \begin{align} & \text{P}\left( \text{private} \right)\text{ = }\frac{\text{students of private college}}{\text{total students}} \\ & =\frac{98}{350} \end{align} And the probability that a student is from a high income family is: \begin{align} & \text{P}\left( \text{high income} \right)\text{ = }\frac{\text{students from high income family}}{\text{total students}} \\ & =\frac{50}{350} \end{align} And the probability that a student is from a high income family and attends private college is: \begin{align} & \text{P}\left( \text{high income and private} \right)\text{ = }\frac{\text{students from high income family, attends private college}}{\text{total students}} \\ & =\frac{28}{350} \end{align} Then, the probability that a student attends a private college or is from a high-income family is: \begin{align} & \text{P}\left( \text{high income or private} \right)\text{ = P}\left( \text{private} \right)+\text{P}\left( \text{high income} \right)+\text{P}\left( \text{high income and private} \right) \\ & =\frac{98}{350}+\frac{50}{350}-\frac{28}{350} \\ & =\frac{98+50-28}{350} \\ & =\frac{120}{350} \end{align} Solving further we get: $\text{P}\left( \text{high income or private} \right)=\frac{12}{35}$

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