Question

A number cube has sides labeled 1 to 6. Daniel will roll the cube 48 times. How many times should he expect to roll a 5?
times​

Answer 1

Answer:

The expected value of rolling a 5 is 8.

Step-by-step explanation:

The sample space of rolling a standard number cube is:

S = {1, 2, 3, 4, 5 and 6}

The cube is standard, this implies that each side has an equal probability of landing face-up.

So, the probability of all the six outcomes is same, i.e. $\frac{1}{6}$.

Now it is provided that Daniel rolls the cube n = 48 times.

Let the random variable X represent the value on the face of cube.

The probability of rolling a 5 is:

$P(X=5)=\frac{1}{6}$

Compute the expected value of rolling a 5 as follows:

$E(X = 5)=n\times P(X = 6)$

                $=48\times \frac{1}{6}\\\\=8$

Thus, the expected value of rolling a 5 is 8.