There are three ants on different vertices of a triangle What is the probability of collision (between any two or all of them) if they start walking on the sides of the triangle?
Similarly find the probability of collision with "n" ants on an "n" vertex polygon
Every Ant can move in 2 possible directions , backward and forward ( B or F ) , so the whole sample space consists of 8 choices, out of which 2 , namely BBB and FFF are no collision choices.
So probability of not colliding is 2 /8 = 1/4 = 0.25
Sample space:
F F B
F F F
F B B
F B F
B F B
B F F
B B B
B B F
So probability of colliding is = 1 - 0.25 = 0.75
In general case(for 'a' ants on 'a' vertices):
total outcomes = 2 x 2 x 2 x ...a = 2ª
no collision = 2
probability of no collision = 2/2ª
So, probability of collision = 1 - 2/2ª
Every Ant can move in 2 possible directions , backward and forward ( B or F ) , so the whole sample space consists of 8 choices, out of which 2 , namely BBB and FFF are no collision choices.
So probability of not colliding is 2 /8 = 1/4 = 0.25
Sample space:
F F B
F F F
F B B
F B F
B F B
B F F
B B B
B B F
So probability of colliding is = 1 - 0.25 = 0.75
In general case(for 'a' ants on 'a' vertices):
total outcomes = 2 x 2 x 2 x ...a = 2ª
no collision = 2
probability of no collision = 2/2ª
So, probability of collision = 1 - 2/2ª
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Post Answer
Ant can go clock wise and anticlockwise
Reply 2so one ant have a both direction to go and second and third also.
so collision = 3 ant go clock wise + three ant go anti clock wise
1/2 * 1/2 * 1/2 + 1/2 * 1/2 * 1/2
= 0.25
Every Ant can move in 2 possible directions , backward and forward ( B or F ) , so the whole sample space consists of 8 choices, out of which 2 , namely BBB and FFF are no collision choices.
Reply 7So probability of not colliding is 2 /8 = 1/4 = 0.25
Sample space:
F F B
F F F
F B B
F B F
B F B
B F F
B B B
B B F
So probability of colliding is = 1 - 0.25 = 0.75
In general case(for 'a' ants on 'a' vertices):
total outcomes = 2 x 2 x 2 x ...a = 2ª
no collision = 2
probability of no collision = 2/2ª
So, probability of collision = 1 - 2/2ª