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Among many other pieces of information, the U.S. Census Bureau records the race or ethnicity of the residents of every county in every state. From these results, the bureau calculated a "diversity index" that measures the probability that two people chosen at random are of different races or ethnicities. Suppose that the census determined that in a county in Wisconsin 80% of its residents are white, 15% are black, and 5% are Asian. Calculate the diversity index for this county.

Answer :

Answer:

The diversity index is 0.335 or 33.5%

Step-by-step explanation:

Probability index= probability that two people chosen at random are different ethnicity or races.

Let the probability of picking black = p(B) =0.15

probability of picking white= p(W)= 0.8

probability of picking Asian= p(A)=0.05

The probability of picking two people who are of different races or ethnicity can be gotten as:

Probability of picking: (White & Black) OR (White & Asian) OR (Black &Asian) OR (black &white) OR (Asian&white) OR (Asian& Black).

Using the notations given earlier, we can write the diversity index as:

Diversity index=p(W) x p(B)+ p(W) x p(A)+ p(B) x p(A) +p(B) x p(W)+ p(A) x p(W)+ p(A) x p(B)

Fixing the values for each term in the last expression gives:

Diversity index= 0.8x0.15 +0.8x0.05+ 0.15x0.05 +0.15x0.8+ 0.05x0.8+0.05x0.15

Diversity index= 0.12+0.04+0.0075+ 0.12+0.04+0.0075

Diversity index= 0.335 or 33.5%

Hence the diversity index is 0.335 or 33.5%

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