Out of how many people should a group at least consist in order to have that the probability that two persons out of that group are having birthday on the same day, is larger than 1/2?

Oft I must strive with wind and wave, Battle them both when under the sea
I feel out the bottom, a foreign land. In lying still I am strong in the strife;
If I fail in that they are stronger than I, And wrenching me loose, soon put me to rout.
They wish to capture what I must keep. I can master them both if my grip holds out,
If the rocks bring succor and lend support, Strength in the struggle. Ask me my name!

At a nice sun shiny day, a man rowed with his boat to an island in the middle of a big lake. On the island he caught some fish. Then he decides to return with his rowing boat. After 10 meters of rowing he looks behind him, but to his big surprise there is no island anymore. What happend to the island?