The events of rolling a 3 or a 5 are disjoint, so .
Each face has a probability of occurring, so the event of interest occurs with probability . The number of times a 3 or 5 is rolled across 288 trials has a binomial distribution, .
Recall that the expected value of a binomial distribution is . So in this experiment, we should expect to witness approximately instances of rolling a 3 or a 5.
By calculus or elementary geometry, we know that the formula for the volume of a cone, given pi (the constant), its height h and its radius r is: Lets solve this relation for the radius: Now we have found a general formula that gives us the radius of a cone, given its volume and height. We need only substitute height (20in) and pi=3.14 to get the numerical equation: r=0.2185*