Meme Spreading In January 2021, a popular meme regarding a former presidential candidate's winter handwear emerged. Suppose that the meme is created by a single user, who sends it to 20 people on day 1, and that everyone who receives the meme on day 1 sends it to 20 people on day 2, and so on, so that everyone who receives the meme on day į sends it to 20 people on day į + 1. What is the maximum number of people who have received the meme by the end of day 4 (not including the creator)? Briefly justify your answer. Answer:

The Infinite Monkey Theorem states that a monkey hitting keys completely at random on a typewriter for an infinite amount of time will, eventually, type any given text. Even the complete works of William Shakespeare.  Some quotes are truly amazing. Consider the famous quote,  "NOT TODAY"    --Arya Stark That's 9 amazing characters.  Suppose a monkey is seated in front of a KEYBOARD WITH 28 CHARACTERS (one for each of the 26 letters in the alphabet, plus the space bar, and a comma).  Suppose the monkey types only 9 characters completely at random. If X is the number of different 9 character strings it could have typed, then the chances that it typed the quote is one divided by X. What is X?

Phoenix is a hub for a large airline. Suppose that on a particular day, 8,000 passengers arrived in Phoenix on this airline. Phoenix was the final destination for 1,600 of these passengers. The others were all connecting to flights to other cities. On this particular day, several inbound flights were late, and 410 connecting passengers missed their connecting flight and were delayed in Phoenix. Of the 410 who were delayed, 85 were delayed overnight and had to spend the night in Phoenix. Consider the chance experiment of choosing a passenger at random from these 8,000 passengers. Calculate the following probabilities. (Round your answers to three decimal places.) (a) Calculate the probability that the selected passenger had Phoenix as a final destination. (b) Calculate the probability that the selected passenger did not have Phoenix as a final destination. (c) Calculate the probability that the selected passenger was connecting and missed the connecting flight. (d) Calculate the…

After a 30-member battalion fled, the general ordered the battalion to suffer decimation as punishment.  In a decimation, one of out of every ten soldiers is killed.  Assuming they are killed at the same time (so that it doesn't matter what order they are chosen), how many ways can the battalion be decimated?