Here is the set up for a nontraditional casino game. You draw a card from a well

Question

Here is the set up for a nontraditional casino game. You draw a card from a well shuffled full deck and if the card is a king you win $100. The game cost $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 the game? Here is the set up for a nontraditional casino game. You draw a card from a well shuffled full deck and if the card is a king you win $100. The game cost $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 the game?

Explanation / Answer

X: no of trials to get the first success.

Then by the law of geometric distribution, E(x)=1/p <--formula, we use it as we have indentified the distribution to be geometric.

where P is the probability of success in a trial

here p=1/52

so, E(x)=52

then total spent is 2*51-100=2.

I expect to spend $2.

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