Average Number of Arms

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 take a number of people, say 2,000 in a small town.

Now let's say one of these people only has one arm.

So the total number of arms is 3,999.

The average number of arms per person will be:

number of arms  =  3,999  =  1.9995
number of people 2,000

So 2 is above average!

We can now see that 1,999 of the people in our small town will have an above average number of arms. They have 2 arms and the average is 1.9995.

If we meet one person at random from our small town, 1,999 out of 2,000 will have an above average number of arms.

The probability of meeting one of these people is 1,999 out of 2,000. This can be expressed as:

1,999  =  0.9995
2,000

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?