Nine children are seated randomly in three rows of three des

Nine children are seated randomly in three rows of three desks. Let A = \"Al and Bobby sit in the same row.\" and B = \"Al and Bobby both sit at one of the four corner desks.\" Are A and B independent?

Solution

A and B are not independent, because event A cannot happen when B happens.

[Al and Bobby cannot sit together if they both sit on corner desks.]

Thus, as the probability of A is affected by B, then they ARE NOT INDEPENDENT.