1. Suppose I roll four 10-sided dice.

a. What is the probability that I roll at least one 9

the opposite of at least one 9 is no 9's. If I don't get no 9's then I get at least one 9 (and vice versa)

P(at least one 9) = 1 - P(no 9's)

b. What is the probability that I get at least one match (that means I get the same number at least twice)

the opposite of at least one match is all different. If I don't get all different then I get at least one match (and vice versa)

P(at least one match) = 1 - P(all different)

2. I have a bag with 3 red, 3 blue, 3 green and 3 white marbles, and I pick 4 without replacement

a. What is the probability that I get at least one red

the opposite of at least one red is no reds. If I don't get no reds then I get at least one red (and vice versa)

P(at least one red) = 1 - P(no reds)

b. What is the probability that I get at least two of the same color

the opposite of at least two of the same color is all different colors. If I don't get all different colors then I get at least two of the same color (and vice versa)

P(at least two of the same color) = 1 - P(all different colors)

3. I have a regular deck of cards, and I draw 3 without replacement

a. What is the probability that I get at least two of a kind (same number or face card)

the opposite of at least two of a kind is all different kinds. If I don't get all different kinds then I get at least two of the same kind (and vice versa)

P(at least two of the same kind) = 1 - P(all different kinds)

b. What is the probability that I get at least one Jack

the opposite of at least one jack is no jacks. If I don't get no jacks then I get at least one jack (and vice versa)

P(at least one jack) = 1 - P(no jacks)

Next, we calculate the all/no probabilities and subtract to get the answer. See here