Question

benjamin rolls a number cube labeled with the numbers 1 - 6 a total of 12 times. determine the expected value and explain your solution method. sample problem how many of the outcomes do you expect to result in a 1? i would expect 2 out of the 12 outcomes to result in a 1. $\frac{1}{6}(12)=2$ how many of the outcomes do you expect to result in a number greater than 2? > enter the answer in the space provided. use numbers instead of words. explain your solution method. > enter the answer in the space provided.

Explanation:

Step1: Calculate probability of number > 2

The numbers greater than 2 on a 1 - 6 number cube are 3, 4, 5, 6. So there are 4 favorable outcomes out of 6 total outcomes. The probability $P$ of getting a number greater than 2 in a single roll is $P=\frac{4}{6}=\frac{2}{3}$.

Step2: Find expected number of outcomes

The number of rolls is $n = 12$. The expected number of outcomes with a number greater than 2 is the probability of getting a number greater than 2 times the number of rolls. So $E=n\times P=12\times\frac{2}{3}$.
$12\times\frac{2}{3}=\frac{12\times2}{3}=8$.

Answer:

8