Why three cents the most she might have to spend

Question

Ms hernandez comes across a gumball machine one day when she is out with her twins. Of cause, the twins each want a gumball. They also insist on having gumballs of the same color. They don't care what color the gumballs are, as long as they're both the same. Ms Hernandez can see that there are only white gumballs and red gumballs in the machine. He gumballs cost a penny each, and there is no way to tell which color will come out next. Ms Hernandez decides to keep putting in pennies until she gets two gumballs of the same color. Why is three cents the most she might have to spend?

Answer 1

If a red gumball comes out the first time and a white gumball comes out the second time, the mother has spent 2 cents, but the kids want the same color gumball. The mother puts a third penny in and either a red or a white gumball will come out. If a red gumball comes out she puts it with the other red one. If a white gumball comes out she puts it with the other white one. Either way there are two red gumballs and a white one or there are two white gumballs and a red one. The mother spends 3 cents at most to get two of the same color.

 

Answer 2

The machine only has two colors red and white.

The two gumballs have to be the same color.

 

Lets say she puts in the first penny and gets a red gumball

When she puts in the second penny if she gets another red gumball then she does not have to buy more but if she gets a white gumball she will now have one red and one white.

 

Once she puts in the third penny it doesn't matter if she gets a red or white because it will match one of the ones she already has. So the most she will have to spend is 3 cents to get two of the same color