1. ## Probability Coin Question

I flip a fair coin. What is the expected number of attempts it will take for one heads to show up and one tails to show up?

Attempt at a solution: I have been trying to use conditional probability, with E(X) = (sigma from k = 1 to infinity)(E(X|Y = k))(P(Y = k))

Any help is appreciated.

2. Originally Posted by noles2188
I flip a fair coin. What is the expected number of attempts it will take for one heads to show up and one tails to show up?

Attempt at a solution: I have been trying to use conditional probability, with E(X) = (sigma from k = 1 to infinity)(E(X|Y = k))(P(Y = k))

Any help is appreciated.
I guess you can read up on coupon collector problem - that shd give you enough hint. Also I'm not clear about your question, what do you mean by - "one heads to show up and one tails to show up". Plz define the event more precisely.

3. how many flips will it take for at least one head to appear and at least one tail to appear?

4. Originally Posted by noles2188
how many flips will it take for at least one head to appear and at least one tail to appear?
Coupon collector's problem - Wikipedia, the free encyclopedia

Another way to look at it is
There are to mutually exclusive and exhaustive events
E1: H....... (i.e. first flip is H)
E2: T....... (i.e first flip is T)
p(E1)=p(E2)=0.5

Consider only E1. After the 1st flip you need a T. What is the expected number of flips to get a T? Let this be n. (What is n?)
So expected number of flips to get atleast H and T = n+1

Similarly for E2. (use symmetry)

Final answer = p(E1)(n+1) + p(E2)(n+1) = n+1.