Problem 1 [10 pts]: Password Protection Probability is a useful tool in analyzing risk, especially with passwords. For this problem, you may leave your answer as a fraction, but the numerator and denominator can be expressions { e. g. P(5,3)/(520) is allowed At your future co-op, there is a monitor welcoming workers with a picture of the Boston skyline. It would be great if it displayed a picture of Grizz, right] To change the picture, you need the administrator's password. i. ii. You know that passwords at the company are subject to the following rules: You know at your co-op that passwords have the following requirements: 0 Between 6 and 8 characters a Each character is a lowercase letter (az) It turns out the administrator's password was \"password\". What are the chances you guess the password on the rst try? Show all of your work. Oh no! They replaced the picture of Grizz. It would be awesome to put Grizz back on the monitors. However, they updated the requirements for the password. The new requirements are as follows 0 Between 6 and 8 characters a Each character is one of 4 special symbols ($, !, %, ?), lowercase letter (arz), or digits (0-9) 0 At least one character must be a special symbol a At least one character must be a digit It turns out the administrator's password changed, but the password does start with a string of 5 consecutive letters followed by a digit. There can be more of both letters and digits afterward. For example, \"grizzl!\" and \"puppy3y%\" are possible passwords, but \"42?doggo\" and \"grizzll\" are not. What are the chances you guess this new password on the rst try? (Hint: When you look at 8 characters, keep in mind not to overcount by making unique cases.)