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Math Help - sorry one more expected value problem

  1. #1
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    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!
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  2. #2
    MHF Contributor matheagle's Avatar
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    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.
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