A mysterious card-playing squirrel (pictured) offers you the opportunity to join in his game. The rules are:

To play you must pay him $2.
If you pick a spade from a
shuffled pack, you win $9. Find the expected value you win (or lose) per game.

prob(spade) = 13/52 = 1/4

expected value = (1/4)9 = $2.25

I would gladly play with this mathematically challenged squirrel all day long.

To find the expected value, we will calculate the probability of winning and losing and then multiply them by the corresponding amounts gained or lost.

First, let's calculate the probability of picking a spade from a shuffled pack of cards. A standard deck of cards has 52 cards, with 13 spades. Therefore, the probability of selecting a spade is:

P(Spade) = Number of Spades / Total Number of Cards = 13/52 = 1/4

Now, let's calculate the expected value:

Expected Value = (Probability of Winning × Amount Won) - (Probability of Losing × Amount Lost)

Amount Won = $9
Amount Lost = $2

Probability of Winning = P(Spade) = 1/4
Probability of Losing = 1 - P(Spade) = 1 - 1/4 = 3/4

Expected Value = (1/4 × $9) - (3/4 × $2)
Expected Value = ($9/4) - (6/4)
Expected Value = $3/4

Therefore, the expected value per game is $0.75.

To find the expected value, we need to multiply each possible outcome by its respective probability, and then sum up these values. In this case, we have two possible outcomes: either winning $9 by picking a spade or losing $2 if we don't pick a spade.

First, let's determine the probability of picking a spade. A standard pack of 52 playing cards has 13 spades out of the total 52 cards. Therefore, the probability of picking a spade is 13/52, which simplifies to 1/4.

Next, we calculate the expected value by multiplying the outcome by its probability:

Expected value = (Probability of winning × Amount won) + (Probability of losing × Amount lost)

Expected value = (1/4 × $9) + (3/4 × -$2)

Expected value = $2.25 - $1.50

Expected value = $0.75

Therefore, you can expect to win an average of $0.75 per game when playing this card game with the squirrel.

how much will the squirrel expect to have