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%
