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.
Probability- Decision making 2
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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.
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.