# We flip a coin until a tail or five heads in a row occur. What is the number of expected flips?

We flip a coin until a taild or five heads in a row occur. What is the number of expected flips?

I have tried to solve this by first defining 2 random variables: X which is 1/2 if head and 1/2 if tail. Then I build the distribution table for this random variable. I don't know exactly how to define the second radom variable.

How would you approach this problem?

• So... te game is over as soon as one tail occurs? – 5xum Mar 10 '16 at 11:43
• $T\sim \min(Geom(\frac 1 2),5)$. – A.S. Mar 10 '16 at 11:48