Answer: She is not correct, the actual number is 13, this is because there are 8 persons that are wearing a hat and sneakers.
Explanation:
We know that we have a total of 10 people wearing a hat and a total of 11 people wearing, but some of those may be using both (so we can have a number of persons that are included in the 10 wearing a hat and in the 11 wearing sneakers)
In the image you can see that 8 are wearing a hat and also wearing sneakers, so if we add 11 + 10, we are counting those 8 persons two times.
So the actual number of persons that are wearing sneakers or wearing a hat is 10 + 11 - 8 = 13