Q1. According to a research, the probability of your date showing up on time for the first date is 0.7. Since possible outcomes are either "on time" or "not on time", the probability of being "not on time" is 1-P(on time) =1-.7=.3. For the second date, the probability of the same person showing up on time is .9 if he/she was on time for the first date. However, this probability is only .2 if he/she was not on time for the first date. a) Show the probability tree summarizing these trials of showing up on time or not on time for the dates. b) Suppose you are looking for long term relationship with a punctual person, you will be happy if your date is on time for both dates, What is the probability of that happening