In MySQL, you can do this easily with conditional aggregation:
select sum(my_bool = 1) as yes, sum(my_bool = 0) as no from table t;
EDIT:
The percentage is very simple:
select sum(my_bool = 1) as yes, sum(my_bool = 0) as no, avg(my_bool = 0) from table t;
However, your value suggests that you are looking for a ratio, not a percentage. To do this, you need to be careful about dividing by zero:
select sum(my_bool = 1) as yes, sum(my_bool = 0) as no, (case when sum(my_bool = 1) > 0 then sum(my_bool = 0) / sum(my_bool = 1) end) from table t;
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