Question

Give an example of an experiment where the sample space does NOT have that each outcome is equally likely. Explain your reasoning as best you can - why are some outcomes more likely than others?

Answer 1

Suppose, we are doing an expeiment, where we toss up a matchbox, up in the air, and try to predict which side it will land on.

Now, the matchbox has '6' different sides.

But quite eveidently, the probability of landing on all 6 sides are not the same.

This is because, 4 of the 6 sides are side faces, and are very small, in terms of areas; so, the chance of landing on these 6 sides are small.

Whereas, the top and bottom sides have more areas; so, the chance of landing on them are far greater.

So, in this case, the outcomes are not equally likely, as the different faces have different probabilities of landing on them.

So, this is an experiment, where the outcomes in the sample space are not equally likely.