CareerCup

Total 2*2*2 = 8 possible configurations after the three person move randomly from the triangle vertices. Out of these, only two configurations lead to people not meeting with anybody - purely clockwise / anti-clockwise motion. So, Probability of meeting = (8-2)/8 = 0.75

PS: I assume probability that two person meet each other doesn't exclude the probability of one person meeting both the other person (one pair on the edge, other upon reaching the vertex).

Probability of a person moving in a direction is 1/2 and two person is moving in same direction then it will be 1/2*1/2. Total probability is 3*1/4 = 0.75

0.75

This question did not mention the speed of each of the 3 person, and if they will stop running once they reach a corner. The probability could be 1 under some conditions...

We do not know if these three people move at the same speed..
Each person two choices of direction, either clockwise or anti-clockwise;
There are eight configurations altogether.
If they all choose the same direction, they would not meet at all, 2 configurations exist.
(8-2)/8 = 0.75.

Each person can go in one of two directions.

So there are 2*2*2 = 8 possible 'group moves' for these three guys.

From these 8 moves only 2 in which no one meets:
1 - when all three go clockwise
2 - when all three go counter clockwise

So P (no one meets another) = 2/8 = 1/4.

And then:
P (at least two persons meet) = 1 - P (no one meets another) = 1-1/4 = 3/4.

It is 3/4.

My approach was that,

Probability the n'th person goes left: p[n,l]=1/2
Probability the n'th person goes right: p[n,r]=1/2

Since each probability is independent of the other then the overall probability of an outcome is the products of each probability.

So, the probability of them all (here n=1,2,3 for 3 people) turning left is: p[1,l]*p[2,l]*p[3,l]=1/8. Also the probability of them all turning right is: p[1,r]*p[2,r]*p[3,r]=1/8.

The only way that at least one collision occurs is that they don't all turn right or all don't turn left: 1-(1/8+1/8)=1-1/4=3/4.

I think it's 9/11