Over time, you have many conversations with a friend about your favorite actress, favorite musician, favorite book, favorite TV show, and so forth for 100 separate topics. On any given topic, there’s only a 0.02 probability that you agree. If you did agree on a topic, you would consider it to be coincidental.
a. If whether you agree on any two different topics are independent events, find the probability that you and your friend never have a coincidence on these 100 topics.
b. Find the probability that you have a coincidence on at least one topic.