Question

When the isle of flume took its most recent census, the population was 86,675 people. Nobody on the isle has more than 83,109 hairs on his or her head. Determine the probability that at least two people have exactly the same number of hairs on their head

Answer 1

Using the pigeonhole principle, the probability that at least two people on the Isle of Flume have the same number of hairs on their head is 100% due to the population being greater than the maximum number of hair counts.

Step-by-step explanation:

The question involves using the pigeonhole principle to determine the probability that at least two people on the Isle of Flume have the same number of hairs on their head. Given the population of the Isle of Flume is 86,675, and the maximum number of hairs on anyone's head is 83,109, there are more people than possible hair counts.

The pigeonhole principle states that if there are more pigeons than pigeonholes, at least one pigeonhole must contain more than one pigeon. Applying this to our scenario, since there are more people than distinct hair counts, at least one hair count (pigeonhole) must be shared by at least two people (pigeons).

Therefore, the probability that at least two people have exactly the same number of hairs on their head is 100% or a certainty, because the number of possible hair counts is less than the number of people on the Isle.