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This is subparts of a single problem. Please solve all. Solve the problem with step by step detailed explanation. I will upvote after getting proper

This is subparts of a single problem. Please solve all. Solve the problem with step by step detailed explanation. I will upvote after getting proper answer. thanks Take your time, but please give proper solve. Question:

a)_An_n_sided_die_is_rolled._Each_face_has_a_unique_label_from_1_to_n._Let,_X_be_the random_variable_that_denotes_the_number_that_is_on_top_of_the_die_after_it_has landed._Express_the_variance_of_the_variable_X_in_terms_of_n.

b)__An_n_sided_die_is_rolled._Each_face_has_a_unique_label_from_1_to_n._Let,_X_be_the random_variable_that_denotes_the_number_that_is_on_top_of_the_die_after_it_has landed._Determine_P_r(X__n).

c)_Two_10_sided_dice_are_rolled._What_is_the_probability_that_the_sum_of_the_two numbers_that_come_up_on_the_dice_is_a_prime_number?

d)_Two_n_sided_die_are_cast._Each_faces_are_numbered_from_1_to_n._One_die_is_red, one_is_blue._What_is_the_probability_that_the_red_one_doesnt_land_a_number divisible_by_3_and_the_blue_one_doesnt_land_a_number_divisible_by_2?

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