Question

A fair six-sided die is rolled 72 times. Theoretically, about how many times should a roll of "4" occur?
A.
There is no way to tell.
B.
4
C.
17
D.
12

Answer 1

To determine how many times a roll of "4" should occur when a fair six-sided die is rolled 72 times, we can calculate the expected number of times to roll a "4".

Each side of the die has an equal probability of \( \frac{1}{6} \). Therefore, when rolling the die 72 times, the expected number of times to roll a "4" is calculated as follows:

\[
\text{Expected number of "4"s} = \text{Total rolls} \times \text{Probability of rolling a "4"} = 72 \times \frac{1}{6}
\]

Calculating this gives:

\[
72 \times \frac{1}{6} = 12
\]

Thus, the expected number of times a roll of "4" should occur is \( 12 \).

The answer is D. 12.