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 1 or a 6? 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: Determine probability of getting 1

A fair - numbered cube has 6 sides. The probability of getting a 1 on a single roll of a cube labeled 1 - 6 is $p=\frac{1}{6}$.

Step2: Use expected - value formula

The expected - value formula for the number of successes in $n$ trials is $E(X)=np$, where $n$ is the number of trials and $p$ is the probability of success in a single trial. Here, $n = 12$ (the number of rolls) and $p=\frac{1}{6}$. So, $E(X)=12\times\frac{1}{6}$.

Step3: Calculate the result

$12\times\frac{1}{6}=2$.

Answer:

2