Independent events

For each of the three writing prompts below, respond with about 110 – 170 words (about one paragraph each).Prompt 1: Some people believe that a coin is “due” to land heads up if it has just landed tails up three times in a row. Using the concept of independent events, explain why a fair coin is never “due” to land heads up.Prompt 2:Suppose two people are playing a card game. Each person is dealt five cards. After looking at their hands, each player is allowed to trade in three of their cards and get three new cards from the deck. Use the concept of conditional probability to explain why the probability of drawing and Ace has changed since before the initial hands were dealt. You may make up sample hands as part of your explanation.Prompt 3: Perform a quick search for survey results of anything you would like. Make sure the article or report contains some reference to a margin of error. Briefly describe the survey and the results. Then make a guess (or explain, if you know) at what it means to have this margin of error. Try to guess how the researchers could make the margin of error lower.