You have a collection of 50 quarters, one from each of the 50 states. You choose two coins from the collection at random, and toss both coins. The state name is visible on the Tails side only, so if a coin comes up Heads you are not able to see which state coin it is. (a) Let A be the event that at least one of the coins landed Tails. What is the probability of having two Tails, given that A occurred?
(b) There are four states whose name begins with the letter "I". What is the probability that both coins tossed are from an "T" state (regardless of whether they landed Heads or Tails)?
(c) Let A be the event that you do not see the name "Illinois". (Recall that the state name is visible only if a coin comes up Tails.) Let B be the event that one of the coins tossed was the Illinois quarter. Calculate P(B|A).
(d) The letter "G" appears twice in the name "Georgia", and there are 6 other states where the letter "G" appears exactly once. Let X be the total number of G's in the state names for the two coins that were tossed (regardless of whether the coin landed Heads or Tails). Calculate the PMF of X