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A game board is constructed by shading two of the regions formed by the altitudes of an equilateral triangle as shown. What is the probability that the tip of the spinner will come to rest in a shaded region? Express your answer as a common fraction.

 

2) 

 

I draw a card from a standard 52-card deck. If I draw an Ace, I win 1 dollar. If I draw a 2 through 10, I win a number of dollars equal to the value of the card. If I draw a face card (Jack, Queen, or King), I win 20 dollars. If I draw a , my winnings are doubled, and if I draw a , my winnings are tripled. (For example, if I draw the , then I win 16 dollars.) What would be a fair price to pay to play the game? Express your answer as a dollar value rounded to the nearest cent.

 Feb 24, 2018
edited by Maplesnowy  Feb 24, 2018
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Replying a bit late, but for the first one it's \(\frac{1}{3}\)

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 Nov 6, 2018

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