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Hitman42 [59]
2 years ago
5

An ant begins at the top of the pictured octahedron. If the ant takes two "steps", what is the probability it ends up at the bot

tom of the octahedron? Assume a "step" is a journey from one vertex to an adjacent vertex along an edge.

Mathematics
1 answer:
Aleksandr-060686 [28]2 years ago
6 0

Answer:

P_{bottom}=\frac{1}{4}=0.25

Step-by-step explanation:

Starting from the top, the ant can only take four different directions, all of them going down, every direction has a probability of 1/4. For the second step, regardless of what direction the ant walked, it has 4 directions: going back (or up), to the sides (left or right) and down. If the probability of the first step is 1/4 for each direction and once the ant has moved one step, there are 4 directions with the same probability (1/4  again), the probability of taking a specific path is the multiplication of the probability of these two steps:

P_{2steps}=\frac{1}{4}*\frac{1}{4}=\frac{1}{16}

There are only 4 roads that can take the ant to the bottom in 2 steps, each road with a probability of 1/16, adding the probability of these 4 roads:

P_{bottom}=\frac{1}{16}+\frac{1}{16}+\frac{1}{16}+\frac{1}{16}=\frac{4}{16}=\frac{1}{4}

The probability of the ant ending up at the bottom is \frac{1}{4} or 0.25.

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