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

The expected value of rolling a 5 is 8.

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.
`(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)=(1)/(6)`

Compute the expected value of rolling a 5 as follows:

`E(X = 5)=n* P(X = 6)`

`=48* (1)/(6)\\\\=8`

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