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!

Guest Jul 8, 2018

#1**+2 **

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