Answer the questions in the screenshot below. Please ensure your answers are correct. Thank you!

1. If a peanut M&M is chosen at random, the chances of it being of a particular color are shown in the table. Color: Brown Red Yellow Green Orange Blue Probability: 0.3 0.2 0.2 0.2 0.1 ? The probability of randomly drawing a blue peanut M&M is (a) 0.1 (b) 0.2 (c) 0.3 (d) 1.0 According to this distribution, it's impossible to draw a blue peanut M&M. 1. Dr. Stats plans to toss a fair coin 10,000 times in the hope that it will lead him to a deeper understanding of the laws of probability. Which of the following statements is true? A. It is unlikely that Dr. Stats will get more than 5000 heads B. Whenever Dr. Stats gets a string of 15 tails in a row, it becomes more likely that the next toss will be | a head. C. The fraction of tosses resulting in heads should be 1/2 D. The chance that the 10th toss will be a head depends somewhat on the results of the first 99 tosses. E. It is likely that Dr. Stats will get about 50% heads 2. Jane and Derek are applying for summer jobs at a local restaurant. After interviewing them, the restaurant owner says, "The probability that I hire Jane is 0.7, and the probability that I hire Derek is 0.4. The probability that I hire at least one of you is 0.9." What is the probability that both Jane and Derek get hired? (a) 0.1 (b) 0.2 (c) 0.28 (d) 0.3 (e) 1.1 2. A psychologist studied the number of puzzles subjects were able to solve in a five-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a subject. X had the following distribution: 3 Probability 0.2 0.4 0.3 0.1 Using the above data, the mean p of X is a. 2.0 b. 2.3 C. 2.5 d. 3.0 e. The answer cannot be computed from the information given