please answer 7-11

'l." .. 7. (8 points) Let S = {a, b, c, d, e, f} be a sample space, E = {a, b, c}, and F = {b, d, e}. a. Determine the events E n F and E' U F'. b. Are E n F and E' U F' mutually exclusive? 8. (10 points) The employees of a company have four-digit extensions. Extensions ending in 00 are considered favorable because they are easy to remember. Suppose extensions are given out randomly and digits can be repeated. a. What is the probability of having a favorable extension? b. What is the probability of having a favorable extension if the rst digit cannot be 0? 9. (8 points) What is the probability that, in a group of 3 people, at least 2 were born in the same month (disregard day and year)? 10. (8 points) If E and F are independent events, nd P(F) if P(E) = 0.2 and PG? U F) = 0.3. 11. (8 points) A marketing rm randomly sends a mass promotional mailing to 30% of the households in a new market area. From experience the rm knows that the probability of response to a mailing is 0.09. What is the probability that a household receives the mailing and responds