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Nov 2017 p62 q3
2914
A box contains 6 identical-sized discs, of which 4 are blue and 2 are red. Discs are taken at random from the box in turn and not replaced. Let X be the number of discs taken, up to and including the first blue one.
(i) Show that \(P(X = 3) = \frac{1}{15}\).
(ii) Draw up the probability distribution table for \(X\).
Solution
(i) To find \(P(X = 3)\), we need the probability of drawing two red discs followed by a blue disc, i.e., \(P(RRB)\).
The probability of drawing the first red disc is \(\frac{2}{6}\), the second red disc is \(\frac{1}{5}\), and the first blue disc is \(\frac{4}{4}\).