Discrete probability distributions

Question

If you select a red diamond picture card (i,e.) a card that doesn't have a number on it) you win $100. It costs $10 to play this game. What is your expected earnings? if you played this game 10,000 times, what is your expected earnings? 

Answer 1

The chance of picking a diamond picture card (sounds like A,K,Q,or J) is 4/52 or 1/13

 

You win 100(1/13) = 100/13 = $7.69

 

Since you pay $10 to play, your expected earning are 7.69 - 10 = -2.31

 

You will expect to have a loss of $2.31 every time you play

 

2.31 is what you expect to lose every time you play, therefore 10000(2.31) = $23100