Facebook Data Science Question (Expected Payout and Probability) I saw this question on Glassdoor and couldn't seem to find a answer to validate mine anywhere:

You're at a casino with two dice, if you roll a 5 you win, and get paid $10. 
  What is your expected payout? If you play until you win (however long that 
  takes) then stop, what is your expected payout?  

I interpret this as "if at least one of the dice gives you a 5", so expected payout for one roll: 

$(1 - (\frac{5}{6})^2) \times 10$

But I am kind of confused on calculating expected payout until you win. Is it:

$(1 - (\frac{5}{6})^2)^n \times 10$

where you have to indicate the number of rolls? Or is there another way?
I am fairly new to this so I really appreciate your help!
Thanks!
 A: Any interview questions are not like Captcha, they require your engagement in dialog rather than just being a computer. So, for me really two options here and choice is up to interviewer ( i.e. you supposed to ask clarifying questions, this tests your communicative ability ).
First option is when they mean total of 5 when adding 2 dice together.  If so, the probability of a win is 4 / 36 = 1 / 9. Expected payout of 1 toss is $10 / 9.
Expected payout of paying until you win is $10 = $10/9 x (1 - 8/9)^-1. 8/9 being a probability of not winning.
Another option is if it is win $10 if either dice is a 5. Then
first, let's compute the  probability of winning. 
I think it is  1/6 (5 on the 1st dice) + 5/6 (not a 5 on 1st dice) x 1/6 (5 on 2nd dice) = 6/36 + 5/36 = 11/36
Then 
E[Payout 1 toss] = $10 * 11/36 = 110/36
E[Payout pay until win] = 110/36 * (1 + 25/36 + (25/36)^2 ... ) = 110/36 * (1 - 25/36)^-1 = 110/36*(11/36)^-1 = $10
And if I was at that interview I would present both solutions and then ask clarifying questions.
