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
.