Geometric Distributions In the game of Monopoly, when a player is in "jail," it takes a "double" on a pair of dice to get out of jail without paying a fine. We'll call X the number of turns it takes to get out of jail. (Assume that the player is allowed to keep throwing the dice indefinitely.) 1. What are the possible values of X? Is Xdiscrete or continuous? The number of turns it takes to get out of jail, X, has a geometric distribution. Conditions for a geometric distribution: B: Each observation is either a success ( double) or a failure ( not a double ). I: Observations are . independent. N. We're interested in the # of observations required to obtain the first success - # of observations is not fixed S: Each observation has the same probability of success (p= /4) 2. What is the probability that X = 1, that is, it takes one turn for the player to get out of jail? 3. What is the probability that X = 2, that is, the player doesn't get a double until the second turn? 4. Find P(X = 3), that is, the probability that the player doesn't get a double until the third turn. 5. Find P(X = 4). 6. Suppose a flashlight manufacturer determined that on average 2 out of every 50 flashlights are defective. What is the probability that the first defective flashlight is the 5th one tested? The 12th one tested