Question

A number cube with sides numbered 1 through 6 is rolled 12 times. The results are shown in the list.



1, 6, 4, 1, 1, 1, 5, 2, 4, 4, 3, 3

Question 1 Response area with 2 radio buttons within 1 groups.
The number cube landed on 4 ,begin bold,[fewer / more],end bold, times than expected.

Question 2
,begin emphasis,Part B,end emphasis,

In 12 rolls, how many times is the number cube ,begin emphasis,expected,end emphasis, to land on the number 4? Enter the answer in the box.

Question 2 Response area with 1 text input box

Answer 1

To answer your questions, we first need to determine the expected outcome when rolling a fair 6-sided number cube.

**Question 1:**

The expected number of times each number (1 through 6) should land when you roll the cube 12 times is calculated by taking the probability of rolling a particular number (which for each number is \(\frac{1}{6}\)) and multiplying it by the number of trials (which is 12).

**Expected number of times to roll a 4:**
\[
\text{Expected} = 12 \times \frac{1}{6} = 2
\]

Now, looking at the results provided:
- The number 4 appeared **3 times** in the rolls.

So, the number cube landed on 4 **more** times than expected (because it landed on 4 three times instead of the expected two).

**Answer for Question 1:**
The number cube landed on 4, **more** times than expected.

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**Question 2:**

As calculated above, the expected number of times the number cube is expected to land on the number 4 in 12 rolls is:

**Answer for Question 2:**
2 (you can enter this value in the response area).