Maths of coincidence

In What are the chances? we saw how the chance of a rare event occurring could be calculated for specific problems.

Will it be a rollover?

Suppose there are $aN$ lottery tickets sold, each with a chance $1/N$ of winning.

20 People Picking

In Pick a Number - Level 1 we showed there is a 13% chance of a duplicate if 20 people choose a number between 1 and 100.

Give method for calculating that all different numbers chosen, for particular numbers, like 20 out of 100.

N People Picking

In Pick a Number - Level 2 we calculated the probability of a group of 20 people all picking different numbers between 1 and 100. Here we derive a general algebraic approximation.

Three children with the same birthday?

A recent news story featured a family whose three children had all been born on January 29th. But is this so remarkable?

Maternal death coincidence?

Two women admitted to the maternity unit of the Royal Hampshire hospital on December 21st 2007 died of Streptococcus A infections within two days, one on December 23rd and one a day later. In a BBC News article the hospital said "their deaths appear to be coincidental".
So what is the chance of such an event happening by chance alone?

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