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

Guest Jul 8, 2018

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!! :)

MathCuber  Jul 8, 2018

Thank you so much! You were right!!! (Just checked)laughsmiley

Guest Jul 8, 2018

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