In griffith experiments why did the mouse live when injected with heat killed smooth and rough bacteria?

The rough bacteria do not have a polysaccharide capsule so mice lived when injected with this strain.  Smooth bacteria have a polysaccharide capsule that protects the bacteria from the immune system, making them virulent and therefore kill mice.  Heat killed smooth bacteria don't have the capsule and are not virulent.

Explanation:

Streptococcus pneumonia has two types of strains, the smooth strain and the rough strain.  Cells of the smooth strain have a protective polysaccharide capsule which protect the cell against the immune system, making it highly pathogenic.  Cells of the rough strain do not have a capsule to protect them against the immune system, the immune system can easily kill the rough strain.  When the cells of the smooth strain are injected in mice the mouse is killed, and when the cells of the rough strain are injected in mice the mice live.

In the next part of the experiment, the cells of the smooth strain were killed by heat, and when these cells are injected into the mice, the mice lived.  But when the cells of the heat killed smooth strain are mixed with the rough strain and then injected in mice, the mice died.  So the DNA from the heat killed smooth strain transformed the rough strain to the virulent strain.