Suppose that 55% of all adults regularly consume coffee, 45% regularly consume carbonated soda, and 70% regularly consume at least one of these two products.   a. What is the probability that a randomly selected adult regularly consumes both coffee and soda? b. What is the probability that a randomly selected adult doesn’t regularly consume at least one of these two products?

Assume that there is a 66​% rate of disk drive failure in a year.   a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk​ drive, what is the probability that during a​ year, you can avoid catastrophe with at least one working​ drive?   b. If copies of all your computer data are stored on fourfour independent hard disk​ drives, what is the probability that during a​ year, you can avoid catastrophe with at least one working​ drive? a. With two hard disk​ drives, the probability that catastrophe can be avoided is ​(Round to four decimal places as​ needed.) b. With fourfour hard disk​ drives, the probability that catastrophe can be avoided is ​(Round to six decimal places as​ needed.)

According to a recent article on the website www.fivethirtyeight.com, 30% of Americanssay they’re trying to reduce or eliminate gluten in their diets. Suppose you have 50volunteers and are interested in the number of them that are trying to reduce oreliminate gluten in their diets.a.) Find the probability that exactly 20 of the volunteers are trying to reduce oreliminate gluten in their diets. Use the formula.b.) Find the probability that 15 or fewer of the volunteers are trying to reduce oreliminate gluten in their diets. Use the calculator.c.) Find the probability that at least 27 of the volunteers are trying to reduce oreliminate gluten in their diets. Use the calculator.

5. A manufacturer of cell phones purchases batteries from a vendor. It is not uncommon to receive defective batteries from this vendor, thus whenever a shipment is received, a sample of batteries is inspected. For this month's shipment, a random sample of 280 batteries is selected and each battery is inspected. If the proportion of defective batteries sampled is more than 1.5%, the entire shipment will be returned to the vendor. What is the probability that this month's shipment will be returned if the true proportion of defective batteries is 4%?