c4countdown

Every day there is a bus that travels from A to B, taking people who live at A to B. Each day, each resident of A has an equal chance of getting on the bus, and their chance of getting the bus is completely independent of anyone else. There are also thousands of residents of A, so by getting on the bus, no-one is significantly reducing the pool of other people who can get on the bus.

One chap, Jeremy, decides that he is going to count the number of passengers who get the bus on each occasion that he happens to (so including himself but not the driver). After many bus journeys, he sees that the average is a nice round 10. He then speaks to some other people who have done the same. They have all found the same - an average of 10 passengers.

What is the average number of passengers for the bus journey?

Ah, it's me isn't it? It's that one isn't it, where you say "you're driving a bus", and then do all that other crazy shit, and then ask the driver's name, and you're supposed to be all like "wtf?!!1 the driver's name? but what about all the people getting on and off and that??!!".

Yeah, so my answer is Jon.

Did I get it right?

Corby wrote:Ah, it's me isn't it? It's that one isn't it, where you say "you're driving a bus", and then do all that other crazy shit, and then ask the driver's name, and you're supposed to be all like "wtf?!!1 the driver's name? but what about all the people getting on and off and that??!!".

Yeah, so my answer is Jon.

Did I get it right?

No, it's nothing silly like that!

Rats, I really thought I had it there

Corby wrote:Rats, I really thought I had it there

This looks like an algebraic (sp?) puzzle to me.

Again I may as well state the obvious. Is it 10? I can't see any way of determining any other answer with the data we're given.

I would've thought 9, given that he's the tenth person and each person gets on independently of all the others. But maybe I need to think about this more carefully.

dinos_the_chemist wrote:Again I may as well state the obvious. Is it 10? I can't see any way of determining any other answer with the data we're given.

Nope.

Charlie Reams wrote:I would've thought 9, given that he's the tenth person and each person gets on independently of all the others. But maybe I need to think about this more carefully.

This is the correct answer. Each passenger counts an average of 10 passengers but the bus driver counts an average of 9. So why the discrepency? Well, one way of looking at it is that when there are 10 people on the bus, there are 10 people to count, when there are 9 on the bus only 9 will count this. And when there are none, no-one will ever count that (apart from the bus driver). So the bus driver is getting an objective view of the average, whereas the passengers are biasing the count upwards.