4. A particle performs a random walk on the vertices of a cube. At each step it remains where it is with probability, or moves to one of its neighbouring vertices each having probability. Let v and w be two diametrically opposite vertices. If the walk starts at v, find: (a) the mean number of steps until its first return to v, (b) the mean number of steps until its first visit to w, (c) the mean number of visits to w before its first return to v.

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