Probability Problems

Alice, Mieke, and Grace sat on the floor of Brown Hall doing homework and eating a bag of Skittles candy. For the purposes of this math problem, we will say that there were 55 skittles total in the bag and 11 skittles of each flavor. There are 5 different flavors of skittles: cherry, grape, green apple, lemon, and orange. Alice's favorite flavor is grape, Mieke's favorite flavor is green apple, and Grace's favorite flavor is orange. What is the probability that after picking 9 Skittles out of the bag, there would be at least one grape skittle, one green apple skittle, and one orange skittle?
(A very real life problem - ask them and they'll be witnesses)

A vocabulary test has 30 questions. Twenty questions have choices ABCDE as answer options, five questions are true or false, and five questions are fill in the blank with a word bank that has 10 words, which can only be used once. If you guess at every question, what is the probability of getting at least half of the questions right?

Someone's grandmother really likes to plant flowers in her garden. In a mass package of tulip bulbs, only one out of four bulbs sprout on average. She has twenty packages of tulip bulbs. What is the probability that out of the twenty packages, how many will not sprout?

Seven cards are dealt from a deck of cards that do not have any red hearts.
a) What is the probability of getting all face cards?
b) What is the probability of getting only kings?
c) What is the probability of getting only black cards?

A teacher is pondering if they should give his students a free period or not. He decides to play the silly game where he chooses a number between 29 and 72 and his students have to guess. The number he chose is an even integer. What is the probability that his students will choose the right number if they all get three tries?

Of the 1700 students at a school, 908 have pet dogs, 762 have pet cats, and 45 have both pets (even though dogs are much cuter). If a student is chosen at random, what is the probability that they have either pet?

A coin is bent so that the probability of getting tails is 0.59 instead of 0.50. This coin toss is extremely important because it chooses the sides of high school debaters in their final round. They have to choose a preset combination of heads and tails that consists of two tosses in order to call for the affirmative or the negative side. 
a) Draw a tree diagram showing the probability of 3 tosses of the coins
b) Find P(HH), P(HT), P(TT), and P(TH) for the team that you like more