Last night my girlfriend posed a rhetorical question that I mistakenly answered leading to a several hour 'debate'.

Essentially she said "I was at a concert with my mum, and my brother's girlfriend, who bought her tickets independently of us, was sat next to me, what are the chances of that?" With the assumed capacity of the venue to ve 10,000 I answered approximately 1 in 10,000 (more accurately 1 in 9,998).

Several others have been bought into the debate, including some with a 1st Degree in Maths and statistics, but each side is unwilling to accept the others answer (with their answer being 1 in 10,000 multiplied by 1 in 9,999).

To answer this we have established that they both definately buy a ticket for the same event independently, so that's happened already, the question is then, now that they both have a ticket what is the chance of them sitting next to each other? Seeing as her mum was with her, there is only a free seat on one side of her. My logic is that she is definately going to sit somewhere, so thats a given, so the only thing we are working out the probability of is that her friend is in the one free seat next to her, there are 9,998 free seats left after her and her mum have taken 2 seats so I feel the answer is 1 in 9,998. The probability of this 1 event happening.

Their arguement is that there are 2 events, her getting one seat multiplied by her friend getting the one next to her.

So, having established that they are both definately going on the same night, what is the chance of them sitting next to each other??? Please help end the arguing!!!!

Thanks very much.