Starting from (0,0,0) of a moving object in the coordinate space through a series of steps, each step of length one. Each step to the left, right, up, down, forward or backward with equal probability. Determine the probability of the object to the point (2,1,2) is not more than 10 steps.
problem of probabilities in 3D
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probability
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0Have you tried something? Also, this looks like a 3D random walk. You need to find the probability of moving exactly $2$ times on $x$, 1 on $y$, and $2$ on $z$, in any order. Note that at most you can make 2 mistakes towards the goal, because you need to undo it to get to the exact coordinate before 10 steps. – 2017-01-05
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0Actually, this could be a binomial distribution. You have $p_{success}=\frac{1}{6}.$ *One* of the cases is to find $\mathbb{P}(\mathsf{Bi}(5,\frac{1}{6})=5)$. – 2017-01-05