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Nov 2007 p6 q7
2952
Box A contains 5 red paper clips and 1 white paper clip. Box B contains 7 red paper clips and 2 white paper clips. One paper clip is taken at random from box A and transferred to box B. One paper clip is then taken at random from box B.
The random variable X denotes the number of times that a red paper clip is taken. Draw up a table to show the probability distribution of X.
Solution
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:
If a red paper clip is taken from box A and then a white paper clip from box B:
\(x = 0\): 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, \(P(X=2) = \frac{40}{60}\).
