Of the 213 countries or independent economies in the world recognized by the Wor
ID: 3341040 • Letter: O
Question
Of the 213 countries or independent economies in the world recognized by the World Bank, 19% are classified by the World Bank as being developed. Are countries with a large land area (>500,000 km2) more likely to be developed? 23% of all countries are large, and 17% of all countries are both large and developed. Use D to denote the event of a country being developed and L to denote a country being large What is the probability that a country is either large or developed? What is the probability that a large country is developed? Compare this to the probability that any country is developed. What is the probability that a developed country is large? Compare this to the probability that any country is large. In terms of countries, what would it mean to say that D and L are disjoint events? Are they disjoint? In terms of countries, what would it mean to say that D and L are independent events? Are they independent? a. b. c. d. e.Explanation / Answer
A) P(L or D) = P(L) + P(D) - P(L and D)
= 0.23 + 0.19 - 0.17
= 0.25
B) P(D | L) = P(D and L)/P(L)
= 0.17/0.23
= 0.739
This is very high when compared to the probability that a county is developed, indicating that larger countries are more likely to be developed
C) P(L | D) = P(L and D)/P(D)
= 0.17/0.19
= 0.895
This is very high when compared to the probability of a country being large
D) If L and D were disjoint, there would have been no countries that are both large and developed.
P(L and D) = 0 for disjoint L and D
Since P(L and D) = 0.17, the events are not disjoint
E) If L and D are independent, the size of a country wouldnt affect the development. In such cases, P(L) x P(D) = P(L and D)
Here, P(L)x P(D) = 0.19x0.23 = 0.0437
P(L and D) = 0.17
So, the events l and D are not independent
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