F1, precision and recall aren't really relevant to classification problems with equivalent and equally prevalent classes, such as "blue" vs "red" in your example, when you care as much about a red ball being mis-classified as blue as you do the other way around. In that case you would indeed just use the overall accuracy, as you suggested.
These scores are important, though, when one class can be described as "positive", and the other as "negative". A typical example would be a medical diagnostic test, which has to discriminate between sick and healthy people. The precision in that case measures the % of people diagnosed "sick" who really are sick, and the recall measures the % of people who are sick, and correctly identified by the test as such. In a medical context, you might place especially high importance on the recall score, since it's typically worse to miss a sick person than to get a false positive on a healthy person.
Another reason to use precision & recall is when you have skewed classes. If 99% of your examples belong in one class, any classifier can easily achieve 99% overall accuracy by always predicting that class label. But as a percentage of the examples in the rare class, it gets 100% wrong, so the classifier's recall for that class would be 0, and its precision undefined (0/0). If the purpose of the classifier is to pick out cases of the rare class, these scores tell you it does a very poor job, while the accuracy tells you nothing.
(Edit: as pointed out by user7019377, the above assumes that you care about the individual class accuracies and want to optimize those rather than the overall accuracy. If you have skewed classes but you only care about overall accuracy, then once again precision & recall don't matter. Also I might add that you don't necessarily need to compute precision & recall to account for class imbalances - you can also just compute a regular accuracy score separately in each class (and potentially average those accuracy scores).)
These two reasons often go hand in hand. E.g. in the medical context sick people are rare relative to healthy people (esp. for a particular disorder being tested), so I could get very high accuracy by designing a test that just returns "healthy" all the time, but that accuracy would be misleading about the usefulness of the test, and potentially many people would suffer for it.