Consider a game in which you draw playing cards from a standard 52-card deck, one at a time. If a player draws a face card (a jack, a queen, or a king), the player is awarded 10 points. Any other card drawn costs the player 3 points. What is the expected value of drawing a card in this game?

Question

anonymous · Answer

$\text{Expected value}=\displaystyle\sum_{\text{all events}}(\text{probability of event})(\text{points awarded})$

Given this equation, you have (assuming cards are replaced)
$$E=10\left(\frac{12}{52}\right)+(-3)\left(\frac{40}{52}\right)$$