Probability (Multiple independent events: AND)

Calculate the probability of the following sets of events:

You have cupboard full of plates, but you do not have a full set of any dishes. You have 3 blue plates, 6 flowered plates, 2 white plates and 1 green plate.

  1. If you are eating alone, and you choose randomly, what is the probability that you get the green plate?
  2. If you are eating with one other person, what's the probability that you get the green plate and a blue plate?
  3. Or, if you prefer matching plates, what's the probability that you pull out two blue plates?
  4. If you choose randomly, what is the probability that you will pull out 4 flowered plates in a row?
  5. Let's say you hate the flowered plates, what's the probability that you pull 2 blue plates and 2 white plates?
  6. What's the probability of getting 4 non-flowered plates? 

You are playing cards with a friend.  There are 52 cards in a standard deck, divided into 4 suits (13 hearts, 13 spades, 13 clubs, 13 diamonds).  Each suit contains an ace, king, queen, jack, 10, 9, 8, 7, 6, 5, 4, 3, and 2 (there are 4 of each of these cards in each deck). 

  1. What is the probability that you get a pair of aces in your first two cards?
  2. What is the probability that you get 3 kings in the first three cards?
  3. What is the probability that you get a flush, all 5 of the cards in your hand are the same suit?
  4. What is the probability that you get a royal straight (specfically: get the following cards in this order:10, Jack, Queen, King, Ace)?
  5. What is the probability that you get a full house (specifically, first three of a kind and then a pair)?
  6. What is the probability that you get four kings and an ace (in that order)?

Answer Key: