Let the events be defined as follows:

• Event R: A red paper clip is taken from box A.
• Event W: A white paper clip is taken from box A.

Calculate the probabilities for each scenario:

1. If a red paper clip is taken from box A and then a white paper clip from box B:

\(P(R, W) = \frac{5}{6} \times \frac{2}{10} = \frac{10}{60}\)

2. If a white paper clip is taken from box A and then a white paper clip from box B:

\(P(W, W) = \frac{1}{6} \times \frac{3}{10} = \frac{3}{60}\)

Now, calculate the probability distribution of X:

• \(x = 0\): No red paper clips are taken. This occurs when a white paper clip is taken from box A and then from box B. Thus, \(P(X=0) = \frac{3}{60}\).
• \(x = 1\): One red paper clip is taken. This can occur in two ways: either a red paper clip is taken from box A and a white paper clip from box B, or a white paper clip is taken from box A and a red paper clip from box B. The probability is \(P(X=1) = \frac{10}{60} + \frac{7}{60} = \frac{17}{60}\).
• \(x = 2\): Two red paper clips are taken. This occurs when a red paper clip is taken from both boxes. Thus, \(P(X=2) = \frac{40}{60}\).

The probability distribution table is: