Cucumbers

In the morning a green-grocer puts 200 kg cucumbers outside in front of his shop. These cucumbers consists for 99% out of water. Because it is a warm day some water will evaporate. As a result, at the end of the day the cucumbers consist for 98% out of water. How many kg's of these cucumbers are left at the end of the day?

Also having birthday today?

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?

Painting stairs

To enter the house of the professor, you first have to walk up a stairs which consists out of twenty steps. The professor thinks his stairs are boring so he decides to paint them. He buys two colors, yellow and green. Every step will be either painted yellow or green and moreover the professor does not want to have two yellow steps directly after each other. In how many ways can the professor paint his stairs? And what is the name of the professor?