CareerCup

Total no. of ways they can move = 2*2*2 = 8
Only 2 ways (clockwise n anticlockwise) not to collide.

Probability for not to collide = 2/8 = 1/4.
To collide = 1-(1/4) = 3/4 = 0.75
:-)

Out of 8 possibilities there are 2 possibilities where they will never collide ie when they all are moving in the same direction

Therefore probsability 6/8

First of all, it says random direction and not necessarily along the edges only. Now we have two cases at hand:
Case-1: We don't know the speed of the ants.
Answer: We can not determine the probability in any way.

Case-2: Assuming constant and equal speeds.
Answer: The ants will meet only when they travel "equal" distance. This essentially means - they will meet only at the centroid of this equilateral triangle! This is the basic logic behind it. I don't know how to show this in terms of probability. But I will try to present a solution - Assuming that each ant can move in 360 directions (based on 360 degrees of a circle), only ONE direction leads to the centroid of the equilateral triangle. This is true for all the three ants. So, it might be said that the probability of their meeting (assuming 360 directions for each ant), is 1/360 * 1/360 * 1/360.

they have to walk around the triangle in the same direction, so as to not collide
so 1/8 , 1/2 * 1/2 * 1/2

67%. each ant got 2 possibilities. Total is 6 combination. 2 of them cannot meet.

There are 8 possibilities:
L L L
L L R
L R L
L R R
R L L
R L R
R R L
R R R
Because at least 2 ants have the same direction, all 3 will never meet.

I think, the question is for any of the two to meet.

1. Any random direction means they don't have to stay on the edges.

2. Even if 1 is not true, it would depend on their speed.

3. If an interviewer cannot frame a question right, they should go fuck themselves.

As the ants move with the same speed if the move into the triangle they will meet.
as the angle is 60deg in the triangle so the probablity of each ant moving inside triangle is 60/360=1/6

for the three of them
1/6*1/6*1/6

Ignore ants behavior, we are not concerned about area of triangle nor how ants will travel nor where or how fast they will travel. All we want to know is the probability of (consider all) ants meeting.

Assuming ant1 meeting ant2 is same as ant2 meeting ant1.

P(All ants will meet) = (number of ways all ants can meet) / (total number of possible events)

Given three ants a1,a2,a3;
The following events are possible
a. None will meet is = organizing each separately = {a1},{a2},{a3} = 1
b. Two will meet     = organizing two elements together = {a1,a2},{a2,a3},{a3,a1} = 3
c. Three will meet   = organizing all together = {a1,a2,a3] = 1

Probability = 1/5 = .2

Maybe I can convince the interviewer with this solution. The interviewer looks at how you are approaching rather than if you got the solution or not, thats what I believe.

u r an idiot.. Plz read the question thoroughly and the dig deep in ur brain and not post random notions tht u thnk is right.. The answer is they cn nvr meet..

it is 3/4.
Proba that they meet is 1-porbability that they don't meet.
lets calculate the proba that they don't meet :

each can move in 2 directions, which are totally independent so you can multiply...
they are 3, they can move each in two direction :
1/2*1/2*1/2 but this can be in either form left to right or right to Left, so multiply this proba by 2 wich is 1/2*1/2*1/2 *2 = 1/4
remember it is the probability that they don't meet so :

1-1/4 = 3/4

Why assume that the triangle has only sides and not a planar area, where ants can move ? Why not consider that the triangle's complement is also a planar area where ants can move, the question never said ants move along the sides of the triangle ?
Why assume ants have equal speed, and not consider variable speeds ?
The question is bogus... and I do not want to spend time on all assumed versions of it...