Question

You have a triangle with 3 ants on different vertices of the triangle. What is the probability that either 2 of the ants or all of the ants collide if all 3 ants start walking on the sides of the triangle?

Answer 1

Answer:

3 / 4

Step-by-step explanation:

For each ant, there are two choices for which way they walk:  either clockwise or anticlockwise.

So there are 2 × 2 × 2 = 2³ = 8 ways for the ants to start walking (e.g. Fred clockwise, Frank clockwise, Frida anticlockwise, is just one of the eight ways).

Only 2 of these result in there being no collision:  either all the ants walking clockwise, or all the ants are walking anticlockwise.

So 8 - 2 = 6 ways do resut in a collision.

Therefore,

Pr ( collision ) = 6 / 8 = 3 / 4 = 0.75