In the World Bank's World Development Indicators there is a population of 214 countries. These countries can be broken down into income categories (from lowest income to highest income):
|
Income Category
|
Count
|
|
|
|
Low Income (LIC)
|
34
|
|
Lower Middle Income (LMC)
|
50
|
|
Upper Middle Income (UMC)
|
55
|
|
High Income (HIC)
|
75
|
|
Total
|
214
|
Assume that the World Bank wants to take a simple random sample, n = 10, of these countries for a poll on how satisfied countries are, overall, with the Bank's work. Note that this sample will be "without replacement," i.e. once a country is chosen, it is "removed." For probabilities in this question, please show the math (fractions) you are using to solve the final probability. Please report your final answer for probabilities using three decimal places. PLEASE SHOW YOUR WORK.
a) What is the probability that a specific country will be included in the sample? (Hint: it may be easier to find this value by using the rule of complements.)
b) What is the probability that no HIC country will be included in the sample? What is the probability that "at least one" HIC will be included in the sample? (Note that these two outcomes are complements: "none" and "at least one.")
c) What is the probability that no LIC countries will be included in the sample? What is the probability that "at least one" LIC will be included in the sample?