A coin is tossed until a head occurs and the number of tosses required is observed. What is the sample space?

 

The answer is [math]\Omega = \{1,2,3,...\}[/math] and my lecturer said, "one, two, three, till infinite." But if you flip a coin inifite times, wouldn't you expect heads to come up half the time...?

He shouldn't have said that, because it doesn't really make sense. A better way (and what I believe he probably meant) is "one, two, three, and so on".

He shouldn't have said that, because it doesn't really make sense. A better way (and what I believe he probably meant) is "one, two, three, and so on".

 

Exactly....

 

But if you flip a coin inifite times, wouldn't you expect heads to come up half the time...?

 

If we live in a "perfect" world, it would be. Coz in a perfect world there is no probability, everything goes and things either happen or not happen, or happen equal to the percentage of the probability of an even in the "unperfect" world where we live in, where things happen according to the probability.