Chapter 11 - Counting Methods and Probability Theory - 11.6 Events Involving Not and Or; Odds - Exercise Set 11.6 - Page 735: 24

$\displaystyle \frac{12}{67}$

Work Step by Step

Let events A and B be defined as A = " an Independent is chosen" B = " a Green is chosen" A and B cannot occur simultaneously, so they are mutually exclusive. If $A$ and $B$ are mutually exclusive events, then: $P$ ($A$ or $B$) $=P(A)+P(B)$. P($A$)=$\displaystyle \frac{n(A)}{n(S)}=\frac{8}{30+25+8+4}=\frac{8}{67}$ P($B$)=$\displaystyle \frac{n(B)}{n(S)}=\frac{4}{67}$ $P$ ($A$ or $B$) $=\displaystyle \frac{8+4}{67}=\frac{12}{67}$

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