intersections of sets and set operations when calculating probability It is given that at a store $55\%$ of the customers buy product $A$, $40\%$ buy product $B$, $35\%$ buy product $C$, $22\%$ buy both $A$ and $B$, $15\%$ buy both $B$ and $C$, $18\%$ buy $A$ and $C$ and lastly, $10\%$ buy $A$ and $B$ and $C$. I need to find the percentage of customers that do not buy product $A$ but they buy at least one out of the $3$ above mentioned products ($A$, $B$, $C$).
I'm not sure I solved this correctly. In my solution:
$A \cap B=0.22$, $B \cap C = 0.15$, $A \cap C = 0.18$, $A\cap B\cap C = 0.1$. Also:

The way I understood this is that the solution is $1-(A \setminus B\cup C)^c=0.6$.

Your Venn diagram is correct but your final answer is not.
If they buy at least one product, then they are in $A \cup B \cup C $. But they do not buy the product $A$ so they are in $(A \cup B \cup C) \setminus A = (B \cup C) \setminus A = 0.3$
