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A bin has 5 white balls and k black balls in it, where  is an unknown positive integer. A ball is drawn at random from the bin. If a white ball is drawn, the player wins 1 dollar, but if a black ball is drawn, the player loses 1 dollar. If the expected loss for playing the game is 50 cents, then what is k?

 

Thanks for answering!smiley

 Jul 8, 2018
 #1
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Since the expected loss is 50 cents, we know it is more likely to lose than to win. It is also impossible to get -50, and the total difference between the 2 possibilities is 2, 50/200=1/4, so the chance of winning is 1/4 and the chance of losing is 3/4. Since (1/4)*3=3/4,  the amount of black balls are 3 times the amount of white balls, so k=15. 

 

Hope this helps!! :)

 Jul 8, 2018
 #2
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Thank you so much! You were right!!! (Just checked)laughsmiley

Guest Jul 8, 2018

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