Question

A bowl contains 9 red balls and 9 blue balls. A woman selects balls at random without looking at them.

Answer 1

I'll do the first problem to get you started

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Part A

There are 9 red and 9 blue.

The worst case scenario is that she selects 3 red in a row. This means that to be guaranteed to have 3 blue, she must select 3+3 = 6 balls.

It is possible that the first three could be blue, but it likely won't be the case. It's best to plan for the worst case scenario.

Answer: 6

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Part B

The worst case scenario is that she pulls out say a red ball, then a blue, then red, and so on. The alternating color selections mean that we don't have three balls of the same color until we get to selection 5.

We could write the sequence like this

RB RB B

or like this

RB RB R

and we see that regardless of what the fifth selection is, we are guaranteed to have three of the same color. The first four items don't really matter. We could have RB changed to BR and it would be the same idea.

Answer: 5