There are two boxes $A$ and $B$. Box $A$ contains 6 white balls and 4 red balls, and box $B$ contains 8 white balls and 2 blue balls. There are three lottery methods (each ball in each box has equal probability of being drawn): (I) First draw one ball from box $A$; if a red ball is drawn, stop; if a white ball is drawn, then draw one ball from box $B$; (II) First draw one ball from box $B$; if a blue ball is drawn, stop; if a white ball is drawn, then draw one ball from box $A$; (III) Simultaneously draw one ball from each of boxes $A$ and $B$. The prize rules are: Among red and blue balls, if only a red ball is drawn, win 50 yuan; if only a blue ball is drawn, win 100 yuan; if both colors are drawn, still win only 100 yuan; if neither color is drawn, win nothing. Let $E_{1}$, $E_{2}$, $E_{3}$ denote the expected values of winnings for methods (I), (II), (III) respectively. Select the correct option. (1) $E_{1} > E_{2} > E_{3}$ (2) $E_{1} = E_{2} > E_{3}$ (3) $E_{2} = E_{3} > E_{1}$ (4) $E_{1} = E_{3} > E_{2}$ (5) $E_{3} > E_{2} > E_{1}$
There are two boxes $A$ and $B$. Box $A$ contains 6 white balls and 4 red balls, and box $B$ contains 8 white balls and 2 blue balls. There are three lottery methods (each ball in each box has equal probability of being drawn):
(I) First draw one ball from box $A$; if a red ball is drawn, stop; if a white ball is drawn, then draw one ball from box $B$;
(II) First draw one ball from box $B$; if a blue ball is drawn, stop; if a white ball is drawn, then draw one ball from box $A$;
(III) Simultaneously draw one ball from each of boxes $A$ and $B$.
The prize rules are: Among red and blue balls, if only a red ball is drawn, win 50 yuan; if only a blue ball is drawn, win 100 yuan; if both colors are drawn, still win only 100 yuan; if neither color is drawn, win nothing. Let $E_{1}$, $E_{2}$, $E_{3}$ denote the expected values of winnings for methods (I), (II), (III) respectively. Select the correct option.\\
(1) $E_{1} > E_{2} > E_{3}$\\
(2) $E_{1} = E_{2} > E_{3}$\\
(3) $E_{2} = E_{3} > E_{1}$\\
(4) $E_{1} = E_{3} > E_{2}$\\
(5) $E_{3} > E_{2} > E_{1}$