Probability- Decision making 2

Question

Which of the following 3 games of chance should you play?1. Draw a card from a standard deck. If it is an ace, you win $5; if it is red, you win $1 ( a red ace wins $6); anything else, you lose $2.2. Draw a card from a standard deck. If it is a club or a face card, you win $2.50; anything else, you lose $1.3. Draw 2 cards, without replacement, from a standard deck. If they are of the same suit, you win $5; if it is a pair, you win $10; anything else, you lose $2.

Answer 1

In the first game drawing an ace with your first and only draw would be unlikely. If by chance you pull the ace and it is red, you will have $6 or $5 if it is not red. Any other card will cost you $2.20. The odds are high, your cost for not drawing the ace is $2.20, and if you win the payout of $5 or $6 is low, and therefore this game is not an option.

 

The second game only pays you $2.50 to draw a club or face card. If you don't draw one of those two cards, you pay $1.30. The odds are very high in this game, and the payout is very low, so it is not an option either.

 

In the third game, the odds of getting a pair or (2) cards of the same suit are extremely high, so winning this game is unlikely. However, your payout would be $5 or $10 if you win,  but if you lose, you only pay $2. For these reasons this game seems to be the better of the three.

 

 

Answer 2

To be honest, none of the three, the odds are not on your side to win. BUT if you must pick I'd select the second game  - Draw a card from a standard deck. If it is a club or a face card, you win $2.50; anything else, you lose $1.3. Your odds are higher that you'd pull a club or face card over pulling a Ace or 2 of the same suit. I would assume the odds favor the player better which is why the payout is less.