Thread: sorry one more expected value problem

ugh this is proving very difficult for me...

A box contains two gold balls and three silver balls. You are allowed to choose successively balls from the box at random. You win 1 dollar each time you draw a silver ball. After a draw, the ball is not replaced. Show that, if you draw until you are ahead by 1 dollar or until there are no more gold balls, this is a favorable game?

Side question - what determines whether a game is favorable or not?

thank you very much!

favorable should mean that you want to play this game, that you EXPECT to win more than you lose, positive expectation.
DO WE lose a dollar if we slect a Gold?
I assume so, otherwise clearly the expectation is positive, since the rv is nonnegative.

You can write out all the possibilties since there are only 5 balls.
I would think along the lines of how many balls can we pick.
The game can end in one selection with the first ball being silver.
The random variable, I assume is your winnings.