How do you calculate the expected frequency of rolling a 6 on a die in 120 rolls?

To calculate the expected frequency of rolling a 6 on a die in 120 rolls, multiply 120 by 1/6.

When you roll a fair six-sided die, each of the six faces (1, 2, 3, 4, 5, and 6) has an equal probability of landing face up. This probability is 1/6, because there is one favourable outcome (rolling a 6) out of six possible outcomes.

To find the expected frequency, you multiply the total number of trials (in this case, 120 rolls) by the probability of the desired outcome (rolling a 6). Mathematically, this is expressed as:

\[ \text{Expected Frequency} = \text{Number of Trials} \times \text{Probability of Desired Outcome} \]

Substituting the given values:

\[ \text{Expected Frequency} = 120 \times \frac{1}{6} \]

\[ \text{Expected Frequency} = 120 \div 6 \]

\[ \text{Expected Frequency} = 20 \]

So, you would expect to roll a 6 approximately 20 times in 120 rolls of a fair die. This is an average value, meaning that in practice, the actual number of 6s rolled could be slightly higher or lower due to the randomness of each roll. However, over a large number of trials, the actual frequency should be close to this expected value.