How likely is this mutation?
Jelly, 9 bytes
^ị“½¥¢‘İP

Try it online!
Takes input as 2376 instead of acgt respectively. The Footer does this for you
-1 byte thanks to Jonathan Allan!
How it works
^ị“½¥¢‘İP - Main link. Takes the first input on the left and the second on the right
^         - XOR the corresponding elements
  “½¥¢‘   - Yield [10, 4, 1]
 ị        - Index into this array, 1-indexed and modularly
       İ  - Take the inverse of each
        P - Take the product

Why this works




Characters
As integers
XOR
1-index into [10,4,1]
Inverse




aa
2, 2
\$0\$
\$1\$
\$1\$


cc
3, 3
\$0\$
\$1\$
\$1\$


gg
7, 7
\$0\$
\$1\$
\$1\$


tt
6, 6
\$0\$
\$1\$
\$1\$


ac
2, 3
\$1\$
\$10\$
\$0.1\$


ag
2, 7
\$5\$
\$4\$
\$0.25\$


at
2, 6
\$4\$
\$10\$
\$0.1\$


cg
3, 7
\$4\$
\$10\$
\$0.1\$


ct
3, 6
\$5\$
\$4\$
\$0.25\$


gt
7, 6
\$1\$
\$10\$
\$0.1\$