Answer the following questions in a separate sheet of paper then send a picture of your answer 1. A student writes a five question multiplechoice quiz. Each question has four possible responses. The student guesses at random for each question. Calculate the probability for each possible score on the test from O to 5. 2. A manufacturer of halogen bulbs knows that 3% of the production of their 100 W bulbs will be defective. What is the probability that exactly 5 bulbs in a carton of 144 bulbs will be defective? 3. A fair die has four faces numbered one to four. What is the probability of rolling a two exactly three times in ten rolls of the die? 4. Suppose that I fall sick an average of 12 times each year. Me falling sick in any time period will not affect the probability of me falling sick in any other time period. Assume that a month is exactly 1/ 12 of a year. (a) Over any given month, what is the probability that I don't fall sick at all? (b) Over a given month, what is the probability that I fall sick more than once? (c) What is the probability that I fall sick at least once in exactly 8 of the 12 months? (Hint: the months are independent of each other, and therefore we can use the ??distribution.)