In an experiment, Emma is going to spin a fair four-sided spinner numbered from one to four. Chloe says that the expected value of the experiment is 2.5. Emma disagrees as she says it is impossible to spin 2.5 and suggests that the expected value is three. Who is correct and why?
To solve the problem, we’re going to need to think about what expected value means. Expected value means what you think it means intuitively. It’s the value you would expect to get if you spun the spinner over and over and over again.
And so at first, it might seem like Emma is correct. It might seem like the expected value should be three. However, when we find the expected value, we find the average value of a random variable over a large number of experiments. And we don’t round it. We just leave it whatever this average is. In this case, the expected value is two and a half.
Chloe is correct because the expected value is the average result of an experiment after a large number of trials, which is 2.5 in this case. Emma is incorrect because she rounded the expected value.