Math of Games

Question

Inexperienced with teleportation, when GB leaves a particular location on the map below she always seems to end up at random at one of the three other locations. If GB is currently at position A on the map and teleports three times, what is the probability that she will end up right back where she started?

     A

B   C   D

 

Answer 1

27 routes are possible (3 x 3 x 3)

Of these 27 only 6 end at A 

The probability of ending at A is 6/27, or 2/9

Answer 2

If each teleportation causes her to land on any of the 4 stops totally at random, then the probability of her landing at any spot is 1/4.  Since it does not matter where she starts from and each teleportation is independent of the last, the probability of her landing back on A after three teleports would be the same 1/4. The same would be true if she teleported once or if she teleported 1 million times.  As long as the events are independent, the odds will always be the same.