Question

there are three ants in three corners of a triangle? each ant started moving towards another corner what is probability that they wont collide at any place??

answer: they need to travel either clockwise or anticlockwise the probability is 1/4.
my question is how this 1/4 came ? can any one explain??

Answer 1

you have i think 8 possibilities for ants moving left and right yes?

Answer 2

3 ants, to directions each and 2^3=8

Answer 3

like saying "flip a coin, what is the probability you get all head or all tails?'

Answer 4

sample space looks like
( R R R)
(R R L)
(R L R)
(L R R)
(L L R)
(L R L)
(R L L )
(R R R)
with r and l being obviously left and right.

Answer 5

only two of these has all ants going in same direction, namely
( R R R) and
(L L L ) therefore
2/8=1/4
is the answer

Answer 6

hope this makes some sense

Answer 7

hey cool.very very thanks for brief and clear explanation. get an medal.. once again thanks....