WS: Probability Distributions Names: Stat 20 is super fun! 1. Suppose a character is picked at random from this sentence (not including punctuation marks). Make a table for the probability distribution of the character that is picked (either a vowel, consonant, or number). Consider a box with four balls in it, two of which are red and two are blue. The balls are identical, except for their color. Now suppose we draw three times at random ("at random" means that all the balls are equally likely) from this box. For each of the following scenarios, list all the possible outcomes, and make a table showing the probability distribution of these outcomes. 2. We draw with replacement. 3. We draw without replacement. 4. Consider tossing a fair coin four times. Sketch a probability histogram for the number of heads in the four tosses. Make sure to label and title your plot (How many total equally likely outcomes are there in four tosses of a coin? Make sure you get your probabilities correct!) A test consists of 20 multiple choice questions. Each question has 4 answer choices, of which only one is correct, and three are incorrect. You haven't studied at all for this test, and decides to answer all the questions by picking one of the four answer choices at random. What is the probability that 5. you answer eight questions correctly? 6. you answer more than two questions correctly