Sean recorded everyone’s number-cube rolls during the game. 1, 6, 2, 1, 5, 4, 2, 2, 1, 4, 5, 1, 3, 4, 1

He stated that the theoretical probability of rolling a 1 is greater than rolling any other number. Explain Sean’s error.

See below. Sean is in error.

Step-by-step explanation:

There are a total of 15 rolls of the cube.

If we count the number of  1's that are rolled we get  5 which is more than any other number. So the EXPERIMENTAL probability of getting a 1 is 5/15 = 1/3.

But this is NOT the THEORETICAL probability.

If we assume that it is a fair cube then the theoretical probability of a 1  is 1/6.

Each number has an equal theoretical probability of 1/6.

Step-by-step explanation:

we know that

The volume of the figure is equal to the volume of cube plus the volume of the cylinder

step 1

Find the volume of the cube

The volume of the cube is equal to

we have

----> the length side of the cube is equal to the diameter of the cylinder

so

step 2

Find the volume of the cylinder

The volume of the cylinder is equal to

we have

substitute

step 3

The volume of the figure is equal to