An experiment observes an integer uniformly chosen from {1.2, 3.4.5, 6, 7, 8, 9, 10, 11.12} Which of the following pairs of events are independent of each other?
a. A= {1, 2, 3};B= {1, 2, 3, 4, 5, 6}
b. A = {1, 2, 3}; B = {3, 9, 12}.
c. A = {2, 4, 6, 8}:B- {8, 10, 12}
d. A = {1, 2, 3, 4, 5, 6}; B = {7, 8, 9, 10, 11, 12}
e. A = {2.4, 6, 8, 10}; B = {1, 3, 5, 7, 9.11}

Options D & E are independent

Step-by-step explanation:

For any of the options to be independent, they have to be mutually exclusive i.e A ∩ B = 0

A) A ∩ B = {1, 2, 3}. They are not mutually exclusive and so they are not independent.

B) A ∩ B = {3}. They are not mutually exclusive and so they are not independent.

C) A ∩ B = {8}. They are not mutually exclusive and so they are not independent.

D) A ∩ B = 0. They are mutually exclusive and thus they are independent.

E) A ∩ B = 0. They are mutually exclusive and thus they are independent.

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.

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