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

Explanation:

Step1: Find probability of even on one die

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

Step2: Find 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 $P(\text{even on both})=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Step3: Calculate expected number of times

The two - dice are rolled 120 times. The expected number of times an even number appears on both dice is $E = n\times P$, where $n = 120$ and $P=\frac{1}{4}$. So $E=120\times\frac{1}{4}=30$.

Answer:

30