Cats generally do a very good job at catching mice and keeping them away from the main living areas within a home. However, having a cat is not a guarantee that you will not have to deal with an infestation. Mice are often in the hidden areas of a home that cats do not have access to, such as the attic or inside walls. Mice also have a keen sense of smell and can identify a cat even when they do not see it. When this is the case, they can often move throughout a home undetected by a cat.
It is also important to take the personality of a cat into consideration. While some cats love to hunt, others do not. If your cat does not like to hunt, they may not be effective at helping you get rid of an infestation. On the other hand, if your cat is an outdoor pet and likes to hunt, they may bring back their catch as a trophy for you. If the mouse is still alive and the cat brings it into the home, a cat could actually cause a mouse problem rather than get rid of it.