Let $P ( X )$ denote the probability of event $X$ occurring, and $P ( X \mid Y )$ denote the probability of event $X$ occurring given that event $Y$ has occurred. There are 7 balls of the same size: 2 black balls, 2 white balls, and 3 red balls arranged in a row. Let event $A$ be the event that the 2 black balls are adjacent, event $B$ be the event that the 2 black balls are not adjacent, and event $C$ be the event that no two red balls are adjacent. Select the correct options. (1) $P ( A ) > P ( B )$ (2) $P ( C ) = \frac { 2 } { 7 }$ (3) $2 P ( C \mid A ) + 5 P ( C \mid B ) < 2$ (4) $P ( C \mid A ) > 0.2$ (5) $P ( C \mid B ) > 0.3$
Let $P ( X )$ denote the probability of event $X$ occurring, and $P ( X \mid Y )$ denote the probability of event $X$ occurring given that event $Y$ has occurred. There are 7 balls of the same size: 2 black balls, 2 white balls, and 3 red balls arranged in a row. Let event $A$ be the event that the 2 black balls are adjacent, event $B$ be the event that the 2 black balls are not adjacent, and event $C$ be the event that no two red balls are adjacent. Select the correct options.\\
(1) $P ( A ) > P ( B )$\\
(2) $P ( C ) = \frac { 2 } { 7 }$\\
(3) $2 P ( C \mid A ) + 5 P ( C \mid B ) < 2$\\
(4) $P ( C \mid A ) > 0.2$\\
(5) $P ( C \mid B ) > 0.3$