How to calculate the diversity index, the probability that two people chosen at random are of different races or ethnicities? The United States Census Bureau started releasing the results of the latest census. Among many other pieces of information, the bureau recoded the race or ethnicity of the residents of every county in every state. From these results the bureau calculated a 'diversity index,' which measures the probability that two people chosen at random are of different races or ethnicities. The census determined that in a county in Wisconsin, 83% of its residents are white, 8% are black, and 9% are Asian. Calculate the diversity index for this county.

drogaid1d8

drogaid1d8

Answered question

2022-11-16

How to calculate the diversity index, the probability that two people chosen at random are of different races or ethnicities?
The United States Census Bureau started releasing the results of the latest census. Among many other pieces of information, the bureau recoded the race or ethnicity of the residents of every county in every state. From these results the bureau calculated a 'diversity index,' which measures the probability that two people chosen at random are of different races or ethnicities. The census determined that in a county in Wisconsin, 83% of its residents are white, 8% are black, and 9% are Asian. Calculate the diversity index for this county.

Answer & Explanation

Miah Carlson

Miah Carlson

Beginner2022-11-17Added 17 answers

Hints:
There two approaches to to this you can either look at the probability of each case where they are different so:
W B + W A + B W + B A + A W + A B
Alternatively
2 × ( W B + W A + B A )
Since we don't case about the order and WB is equally likely as BW.
Finally
1 ( W W + B B + A A )
Since these some combination must happen with probability 1 (or 100%) and these are the only ones that don't show diversity.
Note: This assumes that having chosen your first person the proportion of the remaining population who share the same race has not changed. This is a fair assumption in this case but may not be where smaller populations are involved.
vedentst9i

vedentst9i

Beginner2022-11-18Added 5 answers

HINT
So you are choosing at random, with result being W (with probability 83%), B(8%) or A(9%).
1.What is the probability to draw W+W? B+B? A+A?
2.What is the probability to draw the same result twice?
3.What is the probability to draw different ethnicities in 2 tries?
4.What is the value of the index?

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