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:
[tex]E(X) = \frac{r}{p}[/tex]
30% of the residents are of Hawaiian ancestry.
This means that [tex]p = 0.3[/tex]
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
[tex]E(X) = \frac{r}{p} = \frac{1}{0.3} = 3.3[/tex]
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
