What is the reproductive success of a biting mosquito?
The amount (percentage) of eggs to mature varies greatly and depends on many factors and off course varies by season.

The correct (but not really satisfying) answer is that from every 100 eggs, between 0 and 100 eggs will mature. On average, this number is greater than 1 (otherwise the species would go extinct), and much smaller than 100 (otherwise the world would drown in mosquitoes). Because the question doesn't include the complete lifecycle, it is not exactly 1, but greater than 1.

Some explanation
Mosquitoes lay eggs in water, and the larvae are easy prey for predatory invertebrates (larvae of dragonflies, beetles etc.) and fish. Many mosquito species choose small, isolated waters (like small pools and plant-pots) where there is likely to be little predation. This however carries a risk: these waters often dry out (reproductive succes 0%), offer little resources (reproductive succes low) and offer no shelter against an unforseen predator (reproductive succes low). If they choose wisely however, reproductive succes can be very high. Because of this large variation, an average number is really not so informative.