1. Suppose a COVID test is 96% sensitive and 95% specific. That is, the test will produce 96% true positive results for those with COVID and 95% true negative results for those without COVID. Suppose that 5.7% of people actually have COVID. If a randomly selected individual tests positive, what is the probability he or she does NOT have COVID?

YOUR ANSWER SHOULD BE BETWEEN 0 AND 100 AND ROUNDED TO 4 DECIMAL PLACES. (e.g. 59.5321 would be 59.5321%)

2. Suppose there are two full bowls of cookies. Bowl #1 has 12 chocolate chip and 28 plain cookies, while bowl #2 has 28 of each. Our friend Fred picks a bowl at random, and then picks a cookie at random. The cookie turns out to be a plain one. What is the probability that Fred picked Bowl #1?

3.On average Tempe, AZ gets rain 26.8 days a year (out of 365 days). Your weather app is predicting rain tomorrow. The app isn't perfect though. It only predicts that it will rain around 92% of the time that it actually does rain, and it will predict rain about 5% of the time that it doesn't rain. What is the probability that it is going to rain tomorrow?

4. Suppose that you like about 58.1% of the movies that you see. Rotten Tomatoes is a website which certifies movies as either "fresh" or "rotten". About 80.8% of movie you like are certified "fresh" on rotten tomatoes, and about 14.9% of movies you do not like are certified "fresh". A new movie you are thinking about seeing is certified "fresh". What is the probability that you will like it?

5. A popular film series has produced 23 films of which 13 have been good. A new film from the series is about to come out, and without any additional information we would assume that the odds it is good is 13 out of 23. Historically, 70.2% of good films have a good trailer and 26.4% of bad films have a good trailer. The new film releases a good trailer. What is the probability that the film is good now?

6. Suppose a drug test is 86% sensitive and 95% specific. That is, the test will produce 86% true positive results for drug users and 95% true negative results for non-drug users. Suppose that 5% of people are users of the drug. If a randomly selected individual tests positive, what is the probability he or she is a user?