3. You are investigating articles from the New York Times and from Buzzfeed. Some of the articles contain fake news, while others contain real news assume that there are only two types of news). Note: for the following questions, write your answer using up to 3 significant figures. (a) Fake news only accounts for 5% of all articles in all newspapers. However, it is known that 30% of all fake news comes from Buzzfeed. In addition, Buzzfeed generates 25% of all news articles. What is the probability that a randomly chosen Buzzfeed article is fake news? [3 pts] 2 of 3 Comework 1 Veadline: Jan 15th, 3:00pm CS 4650/7650 Natural Language Understanding (b) Suppose that 15% of all fake news comes from the New York Times (NYT). Furthermore, suppose that 60% of all real news comes from the NYT. Under all assumptions so far, what is the probability that a randomly chosen NYT article is fake news? (3 pts) (c) Mike is an active reader of the New York Times: Mike reads 80% of all NYT articles. However, he also has a suspicion that the NYT is a bad publisher, and he believes that 25% of all NYT articles are fake news. Furthermore, the NYT generates 30% of all news articles. Under all assumptions so far, what is the probability that a randomly chosen article (from all newspapers) will be from the NYT, will be read by Mike and will be believed to be fake news? (4 pts)