Question

A card is drawn at random from a standard deck of playing cards (no jokers). If the card is a diamond, the player wins $5; if it is not a diamond, the player loses $2.

Answer 1

Explanation:

To find the expected value of the game, we need to multiply the value of each outcome by its probability, and then add up the results. Let's first calculate the probabilities of drawing a diamond and not drawing a diamond:

P(diamond) = 13/52 = 1/4

P(not diamond) = 1 - P(diamond) = 3/4

Now we can calculate the expected value of the game:

E = (5)(P(diamond)) + (-2)(P(not diamond))

E = (5)(1/4) + (-2)(3/4)

E = 5/4 - 6/4

E = -1/4

The expected value of the game is -$0.25. This means that, on average, the player can expect to lose 25 cents per game in the long run.