Suppose that 1 out of 1000 people of a specific country are infected with the deadly X-virus. An inhabitant of that country goes the hospital and gives some blood for a survey. Her blood is checked on the X-virus by a test which gives a correct outcome in 99% of the cases. The test points out that the woman is infected. After the investigation, a doctor tells the woman that he is 99% sure that she is infected with the X-virus. Can the doctor be right by making this worrying statement?

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?

Eric has a perfect spherical shaped apple. With a cilindrically shaped drill bit he removes the core of the apple. A cilindrically shaped hole remains, the center of this hole is exactly at the center of the apple. Eric measures the length of the hole with a piece of rope. It turns out to be exactly 8 cm. What is the volume of the remaining apple?