Bitcoin mining - is it a race and how to not waste resources?
Yes and no:
Yes, the first one to find a block gets the whole reward and the others have wasted their effort. But there is no progress in mining, so every attempt to build a block has the same chance at success. Therefore, your chance at finding the next block is equal to the percentage of mining power you contribute to the network.

Also see: 


How is it that concurrent miners do not subvert each other's work?
What exactly is Mining?
In the ASIC-age, is it worth starting mining Bitcoin at home?