Answers:

1. I have 5 green, 3 yellow and 3 blue marbles in a bag.

a. If I pick 3 (without replacement), what is the probability that they are all green?
(5/11)(4/10)(3/9) = 60/990 = 2/33

b. If I pick 3, what is the probability that none of them is green?
(6/11)(5/10)(4/9) = 120/990 = 4/33

c. If I pick 3, what is the probability that at least one of them is green?
1-(4/33) = (33/33)-(4/33) = 29/33

2. If I roll 3 normal 6-sided dice, what is the probability that

a. I get 4 on all three dice?
(1/6)(1/6)(1/6) = 1/216

b. I don't get 4 on any dice?
(5/6)(5/6)(5/6) = 125/216

c. I get a 4 on at least 1 of the dice?
1-P(no fours) = 1-(125/216) = (216/216)-(125/216) = 91/216

c'. I get at least a 4 (4 or greater) on at least 1 of the dice?
1-P(all dice are less than 4)=1-(3/6)(3/6)(3/6)=1-(1/2)(1/2)(1/2)=1-1/8=7/8

d. I get the same number on all three dice?
(6/6)(1/6)( 1/6) = 6/216 = 1/36

e. I don't get the same number on all three dice?
1-P(I do get the same # on all three) = 1-(1/36) = (36/36)-(1/36) = 35/36

f. I get different numbers on each die?
(6/6)(5/6)(4/6) = 120/216 = 5/9

3. If I pick 3 cards (without replacement) from a normal deck, what is the probability that I will get:
(give answers in decimal form)

a. 3 of a kind (all 3 the same number or same face card)?
(52/52)(3/51)(2/50) = .0024

b. 3 different kinds (A, 1, ..., J, Q, K)?
(52/52)(48/51)(44/50) = .8282

c. none of them is a face card?
(40/52)(39/51)(38/50) = .4471

d. at least one face card?
1-P(no face cards) = 1-.4471 = .5529

e. all will have the same suit?
(52/52)(12/51)(11/50) = .0518

f. not all will have the same suit?
1-P(all same) = .9482

g. I will get 3 different suits?
(52/52)(39/51)(26/50) = .3976