# Chapter 11 - Counting Methods and Probability Theory - 11.6 Events Involving Not and Or; Odds - Exercise Set 11.6 - Page 735: 46

$\frac{117}{174}$

#### Work Step by Step

If A and B are not mutually exclusive events, then P(A or B) = P(A)+P(B) - P(A and B) E: has completed four years of high school only or is a woman A: has completed four years of high school only B: a woman P(A) = $\frac{56}{174}$ P(B) = $\frac{92}{174}$ P(A and B) = $\frac{31}{174}$ P(E) = $\frac{56}{174}$ + $\frac{92}{174}$ - $\frac{31}{174}$ =$\frac{56 + 92 - 31}{174}$ = $\frac{117}{174}$

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