If the population is (arbitrarily) 10,000 people, then 10% of 10,000=1000 over 65s; and 1% of 10,000=1000 with mild heart failure.
Consider 4 groups of people: A, B, C, D.
Let A+B=1000 be the over 65s (65+), and B+C=100 be those with heart failure (HF). (D are under 65 and don't have heart failure. A+B+C+D=10000.) B are 65+ + HF=10.4% of (A+B)=104.
The number of people who are 65+ or HF, but not both=(A+B)+(B+C)-B=A+B+C=1000+100-104=996.
996/10000=0.0996 or 9.96%, the probability of 65+ or HF. (D=10000-996=9004, under 65 and no HF.)