Question

You are playing a game where you draw a card from a standard deck, and you will win $13 if you draw a face card,

$3 if you draw an ace and lose $5 if you draw any other card. What is the expected gain from this game?

Round your final answer to the nearest cent.

Answer 1

Explanation:

win

There are 3 face cards / suit. Every suit contains a Jack, Queen, and king.

There are 4 suits so the number of face cards is 3*4 = 12

There is 1 ace / suit

There are 4 suits so the number of aces is 1 * 4 = 4

The gain from the face cards = 12 * 13 = 156

The gain from the aces = 4 * 3 = 12

Total gain = 168

Losses

Any other card costs you $5

How many cards is that? 52 - 16 = 36

Each one costs 5 dollars

Total loss = 5 * 36 = 180

So each time you play the game, you can expect to lose 180 - 68 = 12 dollars. You should walk away quickly from this one.