Question

Suppose that on the leeward side of the island of Oahu, in the small village of Nanakuli, about 30% of the residents are of Hawaiian ancestry. Let ​n = 1, 2, 3,… represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village of Nanakuli. What is the expected number of people you must meet until you encounter the first person of Hawaiian ancestry in the village of Nanakuli? Round your answer to the nearest hundredth.

Answer 1

Answer:

The expected number of people you must meet until you encounter the first person of Hawaiian ancestry in the village of Nanakuli is 3.3

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they are of Hawaiian ancestry, or they are not. The probability of a person being of Hawaiian ancestry is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution:

The expected number of trials to find r sucesses, with p propability, is given by:

$E(X) = \frac{r}{p}$

30% of the residents are of Hawaiian ancestry.

This means that $p = 0.3$

What is the expected number of people you must meet until you encounter the first person of Hawaiian ancestry in the village of Nanakuli?

This is E when r = 1. So

$E(X) = \frac{r}{p} = \frac{1}{0.3} = 3.3$

The expected number of people you must meet until you encounter the first person of Hawaiian ancestry in the village of Nanakuli is 3.3