a box contains 100 red chips, 100 white chips, and 100 blue chips! without looking, whit is the minimum number of chips that must be drawn out to be assured of getting:
a) 30 chip of one color?
b)10 chips of each color?
a) 88. Worst case: draw 29 of two colors before drawing 30 of the third color.
b) 210. Worst case: draw all 100 of two colors, and then draw ten of the third color.
To determine the minimum number of chips that must be drawn out to be assured of getting a certain number of chips of a specific color, we can calculate the worst-case scenario. In this case, we assume that we draw chips of all other colors until we have only the desired color left.
a) To be assured of getting at least 30 chips of one color, we need to consider the worst-case scenario, where the first 99 chips drawn are either red or blue, and the 100th chip is the remaining color (in this case, white). Therefore, we need to draw a minimum of 99 + 1 = 100 chips to be assured of getting 30 chips of one color.
b) To be assured of getting at least 10 chips of each color, we need to consider the worst-case scenario, where the first 9 chips drawn are red, the second set of 9 chips drawn are white, and the third set of 9 chips drawn are blue. After drawing these 27 chips, it is possible that none of them is of any particular color, which means we need to draw an additional chip of each color to achieve a minimum of 10 chips of each. Therefore, we need to draw a minimum of 27 + 3 = 30 chips to be assured of getting 10 chips of each color.