The following is a probability distribution table of a certain population.

$X$	1	2	3	Total
$\mathrm { P } ( X )$	0.5	0.3	0.2	1

When a sample of size 2 is drawn with replacement from this population, the probability distribution table of the sample mean $\bar { X }$ is as follows.

$\bar { X }$	1	1.5	2	2.5	3
Frequency	1	$a$	$b$	2	1
$\mathrm { P } ( \bar { X } )$	0.25	$c$	$d$	0.12	0.04

Find the value of $100 ( b + c )$. [4 points]

Show that if $\frac { 1 } { n ^ { 2 } } = \mathrm { o} \left( p _ { n } \right)$ in the neighborhood of $+ \infty$, then $\lim _ { n \rightarrow + \infty } \mathbf { P } \left( A _ { n } > 0 \right) = 1$.