Another book and the maths taster day

I was looking through different internet forums to gain an idea of the sort of arguments around randomness. One person suggested this book:
Chaos by James Gleick

Yesterday (Monday 12th July), I attended a maths taster day at Queen Mary University of London. The topic was Inevitable patterns in mathematics. The lecturers were Ben Green and Imre Leader.
1) Misleading patterns
- Birthday coincidences: There were about 50 of us at the taster day. The lecturer called out all the months of the year and asked us to raise our hand when he said the month that our birthday was in. The most popular month was September, so he made all the students who had birthdays in September stand up. This included me. The then asked us what date in September we were born in, and if no one else shared that birthday, the person would sit down. When he came to me, I stated that my birthday was on the 17th of September and funnily enough, another girl who was standing up said that she was also born on that day.
I was very surprised that out of a group of 50 people, it was possible that two people shared the same birthday. As Imre Leader later explained, it was almost certain that two people would share the same birthday: The probability that there is a repeated birthday ina group of 50 people is 1-(365/365)(364/365)(363/365)(362/365)...(316/365) which is around 0.97.