To determine how many times the number cube landed on 4 compared to what we would expect, we first need to calculate the expected frequency of rolling a 4 when rolling the cube 12 times.
A fair number cube (with sides numbered from 1 to 6) will have an equal probability of landing on each number. Therefore, the probability of rolling a 4 is:
\[ P(\text{rolling a 4}) = \frac{1}{6} \]
With 12 rolls, the expected number of times we would roll a 4 is:
\[ \text{Expected number of 4s} = 12 \times \frac{1}{6} = 2 \]
Next, we count how many times 4 appears in the given results:
The list of rolls is: 1, 6, 4, 1, 1, 1, 5, 2, 4, 4, 3, 3.
From this list, we can see that the number 4 occurs 3 times.
Now we can compare the actual number of times a 4 was rolled (which is 3) to the expected number (which is 2):
\[ \text{Difference} = \text{Actual} - \text{Expected} = 3 - 2 = 1 \]
Therefore, the number cube landed on 4 1 time more than expected.
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