$7枚硬币的面值由小到大排列为0.1,0.1, 0.5,0.5,1,1,5。$
$列出所有可能的和: 0.1+0.1=0.2,0.1+0.5=0.6,0.1+0.5=0.6,0.1+1=1.1,$
$0.1+1=1.1,0.1+5=5.1 (6种)\ $
$0.1+0.5=0.6,0.1+0.5=0.6,0.1+1=1.1,0.1+1=1.1,0.1+5=5.1 (5种)$
$0.5+0.5=1,0.5+1=1.5,0.5+1=1.5,0.5+5=5.5 (4种)$
$0.5+1=1.5,0.5+1=1.5,0.5+5=5.5 (3种)$
$1+1=2,1+5=6 (2种)$
$1+5=6 (1种)$
$6+5+4+3+2+1=21(种)$
$1÷21=\frac{1}{21}$
$答:和是1角的可能性是\frac{1}{21}。$