Question

A standard number cube is rolled 288 times. Predict how many times a 3 or a 5 will be the result.

Answer 1

The events of rolling a 3 or a 5 are disjoint, so $\mathbb P\bigg((X=3)\cup(X=5)\bigg)=\mathbb P(X=3)+\mathbb P(X=5)$.

Each face has a $\dfrac16$ probability of occurring, so the event of interest occurs with probability $\dfrac16+\dfrac16=\dfrac13$. The number of times a 3 or 5 is rolled across 288 trials has a binomial distribution, $\mathcal B\left(288,\dfrac13\right)$.

Recall that the expected value of a binomial distribution $\mathcal B(n,p)$ is $np$. So in this experiment, we should expect to witness approximately $\dfrac{288}3=96$ instances of rolling a 3 or a 5.