Welcome to your probability interview! In a quantitative finance interview, one of the most important things is to explain your thoughts. A good thought process is worth more than a correct answer with no ability to articulate your reasoning. This quiz is no different, as we’ll be breaking down two problems into their logical steps.

For the first problem, consider the following:

A \(3\times 3\times 3\) cube is painted red, and then cut into 27 \(1\times 1\times 1\) cubes. One of these cubes is chosen at random, and rolled like a die. What is the probability that it lands with a painted side facing up?

First of all, what is the total area that has been painted red?

For the second problem, consider the following:

There are two boxes, each with three balls. Box A has two red balls and one blue ball; Box B has one red ball and two blue balls. I randomly choose a box, and randomly draw a red ball. If I then draw another ball from the same box, what is the probability that it is also red?

Wrapping things up, what is the answer to the probability question below? Keep in mind that there is no replacement.

There are two boxes, each with three balls. Box A has two red balls and one blue ball; Box B has one red ball and two blue balls. I randomly choose a box, and randomly draw a red ball. If I then draw another ball from the same box, what is the probability that it is also red?

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