# Probability Coin Question

• Nov 17th 2009, 08:13 PM
noles2188
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.
• Nov 17th 2009, 10:39 PM
aman_cc
Quote:

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.
• Nov 17th 2009, 10:48 PM
noles2188
how many flips will it take for at least one head to appear and at least one tail to appear?
• Nov 17th 2009, 10:49 PM
aman_cc
Quote:

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