There are 8 black balls and 8 white balls in a box and cannot be seen through:
• How many balls must be picked up in order to guarantee there are three balls having the same color
• How many balls must be picked up in order to guarantee there are three white balls
guarantee same color?
worse case, you pick alternative colors.
w b w b then the next has to be w or b. Five.
for three white? Worse case, You have to pick all the black first, so 11.
thank you.
To determine the minimum number of balls that must be picked up to guarantee there are three balls of the same color, we need to consider the worst-case scenario.
1. To guarantee there are three balls of the same color:
In the worst case, imagine that every time you pick up a ball, it is of the opposite color to the previous ones you picked up. In this scenario, you could pick up 8 black balls, followed by 8 white balls, and then the next ball you pick up would complete a set of three balls of the same color. Therefore, you would need to pick up a total of 17 balls to guarantee there are three balls of the same color.
2. To guarantee there are three white balls:
Similarly, in the worst-case scenario, imagine that every time you pick up a ball, it is a black ball. You could pick up 7 black balls, and then the next two balls you pick up would be the first two white balls. Therefore, you would need to pick up a total of 9 balls to guarantee there are three white balls.
Please note that these answers assume that you will not see the color of the balls you pick up until you have selected the required number.