Average Number of Arms

The question is:

What is the probability that the next person you meet has
an above average number of arms?

Is it:

Impossible
Unlikely
Likely
Very Likely
Certain

Solution

Let's imagine a small town of 200 people.

Now let's say one of them has only one arm:

So the total number of arms is 399

The average number of arms per person is:

number of armsnumber of people = 399 arms200 people = 1.995

So 2 is above average!

We can now see that 199 of the people in our small town have an above average number of arms: they have 2 arms and the average is 1.995

If we meet one person at random from our small town, then 199 out of 200 will have an above average number of arms.

The probability of meeting one of these people is 199 out of 200. This can be expressed as:

199200 = 0.995

If the probability was 1.0 it would be certain that the next person we meet would have an above average number of arms. It is not 1.0 but it is close. So we can say that it is:

Very Likely that the next person we meet will have an above average number of arms.

 Not quite what you expected, hey?