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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.

There are $115,226,802$ households in the US. $58$% of households have at least $1$ musician. $43$% have $2$ or more musicians. How many musicians are there?

The action for this problem takes place in an island of Knights and Knaves, where Knights always make true statements and Knaves always make false statements and everybody is either a Knight or a Knave. Two friends A and B lives in a house. The census taker (an outsider) knocks on the door and it is opened by A. The census taker says ''I need information about you and your friend. Which, if either of you, is a Knight and which, if either of you, is a Knave?" "We are both Knaves" says A angrily and slams the door. What, if any thing can the census taker conclude?
a.A is a Knight and B is a Knave.
b.A is a Knave and B is a Knight.
c.Both are Knaves.
d.Both are Knights.
e.No conclusion can be drawn.
Not able to grasp it please someone help me

The Canadian Tobacco Monitoring Survey is a national survey administered by Statistics Canada to study smoking trends of Canadians aged 15 or older. The most recent survey found that 19% of Canadians aged 15 years or older smoke on a daily basis. In addition, 22% of men are smokers, and 16% of women are smokers.
The most recent census shows that men make up 50% of the Canadian population, with women making up the remainder.
You randomly pick a Canadian that is 15 years old or older. What is the probability this person
a) Is male and a smoker?
b) is a women and not a smoker?
c) What percentage of smokers are male?
d) What percentage of smokers are women?
I think I've got 1/2 of a probability table figured out,
P(Male) = 0.5
P(Male complement) = 0.5,
P(Smoker) = 0.19
P(Smoker Complement) = 0.81
I'm just stuck on how to fill in the middle. Would appreciate any help!

The article “Statistical evidence of discrimination” (J. Ameri. Stat. Assoc., 1982, 773-83) discussed the court case of Swain v Alabama (1965), in which it was alleged that there was discrimination against blacks in grand jury selection. Census data suggested that 25% of those eligible for grand jury service were black, yet a random sample of 1050 individuals called to appear for possible duty yielded only 177 blacks. Given this observation the court believed that there wasn’t enough evidence to establish a prima facie (without further evidence) case. Would you agree with the court’s decision?

Estimating number of slaves imported before 1790
I have a statistics problem I am having a hard time figuring out how to model mathematically.
The 1790 US Census counted 697,681 slaves and 59,196 free Africans in the United States.
(A) assume importation began in 1620 and increased according to some unknown exponential function
(B) assume a rate of natural increase at 2.5% per annum
(C) assume all free Africans are manumitted slaves or their descendants and the rate of manumission is constant during the entire period
Given these assumptions, what is the function that would describe the annual number of slaves imported during that time (1620-1790)?