Here is the setup for a non-traditional casino game: You draw a card from a well
ID: 3057533 • Letter: H
Question
Here is the setup for a non-traditional casino game: You draw a card from a well shuffled full deck and if the card is a king you win $100. The game costs $2 to play and you decide to play the game until you win the $100. Each time you draw a card you pay $2, and if the card is not a king, the card is put back in the deck, and the deck is reshuffled. How much money should you expect to spend on this game?
The answer is $26 - I just don't know how this amount is derived. Please be specific with which statistical technique is used to determine this.
Explanation / Answer
A complete deck has 52 cards, out of which 4 are kings.
So there is a 1 in 13 chance of drawing a king. Thus the expected number of draws it will take to draw a king is 13.
So, expected amount of money that will be spent on this game = Expected number of draws*Payment per draw = 13*2 = 26 dollars
Hope this helps !