Infinite Sample Spaces 9/29

Example: Toss a coin until heads comes up.

$$\Omega=\{1,2,3,\ldots \}$$

Looking at the tree diagram, we see that P(1)=1/2, P( 2 )=1/4, P(3)=1/8........

The distribution function in this case is: m(i)=1/2ⁱ

But we have to check that $\sum_\omega m(\omega)=1$

What is the probability that heads turns up after an even number of tosses?