Puzzle Nekst 4 2014-2015

The summer holiday is right around the corner, which means that weeks filled with sunshine, spare time and vacations are almost upon us. For those of you who cannot stand the idea of not having lectures concerning mathematical problems, we have created an interesting puzzle concerning a somewhat peculiar topic: the flu.

To celebrate the start of the summer holidays, company X organizes a great feast for its hundred employees. Right before dinner starts though, it turns out that their main chef has the flu. Unfortunately, while preparing the first course – a delicious broccoli soup – the chef sneezes and exactly fifty droplets of nasal discharge find their way into the soup.

As there is no time to prepare another soup, the chef decides to serve the broccoli soup anyway. He stirs it one more time, making the droplets disperse randomly through the soup, after which he gives a bowl of soup to all of the hundred employees. No soup is left in the soup pot. Now the question we wish to answer is: what is the expected amount of bowls that will be infected, i.e. the number of bowls that have at least one droplet of nasal discharge in it?

Please send your solution to Nekst@Asset-Econometrics.nl before October 1. A crate of beer or a delicious pie, whichever the winner prefers, will be waiting for whoever has the best (partial) solution. Please note that, as before, every recipient of this magazine is eligible to send in their solution, so members of the department are invited to participate as well. Good luck!

Stan Albers is the winner of the previous puzzle. As a reward, he can come and pick up a crate of beer or a pie at room E1.10. The solution of the previous puzzle was unspecified