Question: A group of six children uses the procedure described below to determine which of the six will play first with a new toy. Six identically-looking matches are used. An uninvolved person secretly breaks one match at its lower end and then holds all six in her palm, so that the lower ends are hidden, and only the six upper ends are visible. The first child randomly draws a match. If the match is the broken one, the child is selected, and the drawing procedure stops. If not, the second child draws a match, and on on. The drawing procedure terminates when the broken match is selected. Let us denote the six children by their ordinal numbers in the draw: \(1,2, \ldots, 6\). For each child. compute the probability that he or she will be selected to play with the new try.

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