Suppose that a non-fair coin with

is tossed repeatedly.

(a) What is the probability that the first time we get "Heads" happens on an even numbered toss?

(b) What is the probability that the first "Heads" occurs on an odd-numbered toss?

(c) Explain why the answer (b) is larger than the answer in (a). Does it depend on

?

So let

denote the probability that the first head appears on the

th toss. Then

In general,

. So for part (a) it would be

where

.

Similarly, for part (b) it would be

where

.

So

and

.

Then

. Then

?

It seems like

.