Probability of ball hitting the fan Case 1: A person throws a ball upwards to hit a fan which is not rotating. Let the probability of the event of ball hitting the fan be $p_1$.

Case 2: Same person now does the same experiment, this time with a rotating fan. Let the probability of the event this time be $p_2$.

Then what is the relationship between $p_1$ and $p_2$?
$$P(2)&gt;P(1)$$ 

In order to exist, the ball must have some radius $r$. 

Now, as the ball passes through the plane on which the fan rotates, time passes (the amount depending on both the radius of the ball and its initial velocity).

Given that any amount of time passes while the ball is passing through the plane, even a terribly small amount of time, the fan rotates at least a very small distance, meaning it covers greater area than if angular velocity $\omega=0$.

Thus, the probability $P(2)$ must exceed that of a stationary fan $P(1)$ since having a nonzero radius is a necessary condition for the ball to exist.
$p(1)=p (2)$ same percent of ceiling is always covered by the fan at any time