Question

Suppose there are 30 ants are uniformly and randomly spread across a 10 inch wide linear stretch. A mean child decides to hold a magnifying glass over the entire 10 inch stretch and any ants under the magnifying glass for 5 seconds will die. Assuming the ants travel at 1 inch per second, what is the probability that 6 or fewer ants will die?  

Answer 1

As the ants travel at 1 inch per second and we will assume here that all the ants move towards one of the direction of the linear stretch, the probability that the that a particular ant die is computed as the probability that the ant is at least 5 inch from the side from which they can escape.

= 5 / 10 = 0.5

Therefore the number of ants who die here is modelled here as:

The probability that 6 or fewer ants die is computed here as:
P( X <= 6)

This is computed using EXCEL as:
=binom.dist(6,30,0.5,TRUE)

0.0007 is the output here.

Therefore 0.0007 is the required probability here.