Question

the faces on a six - sided die are labelled 1, 2, 3, 4, 5, 6. the die is rolled 18 times. how many times should you expect to roll a 6? a) 12 b) 6 c) 3

Explanation:

Step1: Calculate probability of rolling a 6

The probability $P$ of rolling a 6 on a fair six - sided die is $\frac{1}{6}$ since there is 1 favorable outcome (rolling a 6) out of 6 possible outcomes.

Step2: Use expected - value formula

The expected - value formula for a binomial situation is $E = n\times P$, where $n$ is the number of trials and $P$ is the probability of success in a single trial. Here, $n = 18$ (number of die rolls) and $P=\frac{1}{6}$. So, $E=18\times\frac{1}{6}$.

Step3: Calculate the result

$18\times\frac{1}{6}=3$.

Answer:

c) 3