Question

two dice are rolled 120 times. how many times would you expect an even number to appear on both dice? ? times

Explanation:

Step1: Calculate probability of even on one die

A die has 6 faces. The even - numbered faces are 2, 4, 6. So the probability of getting an even number on one die, $P(\text{even on one die})=\frac{3}{6}=\frac{1}{2}$.

Step2: Calculate probability of even on both dice

Since the rolls of the two dice are independent events, the probability of getting an even number on both dice is the product of the probabilities of getting an even number on each die. So $P(\text{even on both dice})=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Step3: Calculate expected number of times

The number of trials $n = 120$. The expected value $E$ of an event with probability $p$ in $n$ trials is given by $E=np$. Here, $n = 120$ and $p=\frac{1}{4}$, so $E=120\times\frac{1}{4}=30$.

Answer:

30