What is the expected frequency if the probability is 0.5 in 80 trials?

The expected frequency is 40 if the probability is 0.5 in 80 trials.

To understand this, let's break it down. The expected frequency is a way of predicting how often an event will occur based on its probability. In this case, the probability of the event happening is 0.5, which means there's a 50% chance of it occurring in any single trial.

When you have 80 trials, you can calculate the expected frequency by multiplying the probability by the number of trials. So, you take 0.5 (the probability) and multiply it by 80 (the number of trials).

\[ \text{Expected Frequency} = \text{Probability} \times \text{Number of Trials} \]
\[ \text{Expected Frequency} = 0.5 \times 80 \]
\[ \text{Expected Frequency} = 40 \]

This means that out of 80 trials, you would expect the event to occur 40 times. It's important to remember that this is an average expectation. In real life, the actual number of occurrences might be slightly different due to random variation, but over a large number of trials, the average should be close to the expected frequency.

Understanding expected frequency is useful in many areas of maths and science, as it helps you predict outcomes and analyse data. For example, if you were flipping a fair coin 80 times, you would expect it to land on heads about 40 times, because the probability of getting heads is 0.5.