two dice are rolled 180 times. how many times would you expect a 5 to appear on both dice? ? times

Answer:

5

Explanation:

Step1: Calculate probability of 5 on one die

The probability of getting a 5 on a single - die roll is $\frac{1}{6}$.

Step2: Calculate probability of 5 on both dice

Since the rolls of the two dice are independent events, the probability of getting a 5 on both dice is $\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}$.

Step3: Calculate expected number of times

The number of trials $n = 180$. The expected value $E=n\times P$, where $P$ is the probability. So $E = 180\times\frac{1}{36}=5$.