QuestionDraw a card from a deck: win \$6 for a face card, \$5 for an ace, lose \$3 for others. Find the probability distribution and expected gain.

Studdy Solution
Calculate the expected gain.
$$(x) =6 \cdot \frac{3}{13} +5 \cdot \frac{1}{13} -3 \cdot \frac{}{13} = \frac{18}{13} + \frac{5}{13} - \frac{27}{13} = -\frac{4}{13}$$The expected gain from this game is $-\frac{4}{13}$ dollars. This means that, on average, the player will lose about $0.31$ dollars each time they play the game.