Question

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

58 times

93 times

96 times

99 times

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
`\frac16` probability of occurring, so the event of interest occurs with probability
`\frac16+\frac16=\frac13`. The number of times a 3 or 5 is rolled across 288 trials has a binomial distribution,
`\mathcal B\left(288,\frac13\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
`\frac{288}3=96` instances of rolling a 3 or a 5.