\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
In a game of chance, a player spins a spinner:
The player wins the amount of money indicated by the arrow, but it costs \(\dollar 5\) to play each game. In gambling, the gain is defined as the payout minus the cost to play.
  • Calculate the expected gain \(E(X)\) of the player (
    ! e \(\pi\) ( ) % AC sin cos tan 7 8 9 / \(\sin^{-1}\) \(\cos^{-1}\) \(\tan^{-1}\) 4 5 6 * \(x^2\) \(\sqrt{\phantom{2}}\) xy 1 2 3 - ln exp log 0 . = +
    ).
  • Interpret the result in terms of the player’s average outcome per game.

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