How do you calculate the expected frequency of getting a 2 on a die in 180 rolls?

To calculate the expected frequency of getting a 2 on a die in 180 rolls, multiply 180 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 desired outcome (rolling a 2) out of six possible outcomes.

To find the expected frequency, you multiply the total number of rolls by the probability of the desired outcome. In this case, you want to know how many times you can expect to roll a 2 in 180 rolls. The calculation is straightforward:

\[ \text{Expected frequency} = \text{Total number of rolls} \times \text{Probability of rolling a 2} \]

\[ \text{Expected frequency} = 180 \times \frac{1}{6} \]

\[ \text{Expected frequency} = 30 \]

So, you can expect to roll a 2 approximately 30 times in 180 rolls of a fair die.

This method uses the concept of expected value, which is a fundamental idea in probability. It helps you predict the average outcome over a large number of trials. Even though you might not get exactly 30 twos in 180 rolls every time, this is the average number you would expect if you repeated the experiment many times.