Help to solve these following ques (underlined)and provide explanations.

Note: Beginner at probabilities

Thank you.

9. A problem on a multiple-choice quiz is answered correctly with probability 0.9 if a student is prepared. An unprepared student guesses between 4 possible answers, so the probability of choosing the right answer is 1/4. Seventy-five percent of students prepare for the quiz, If Mr. X gives a correct answer to this problem, what is the chance that he did not prepare for the quiz? [0.0847] 10. In the system in the following figure, each component fails with probability 0.3 independently of other components. Compute the system's reliability. [0.8854] A B 11. Among 10 laptop computers, five are good and five have defects. Unaware of this, a customer buys 6 laptops. a. What is the probability of exactly 2 defective laptops among them? b. Given that least 2 purchased laptops are defective, what is the probability that exactly 2 are defective? 12 Two out of six computers in a lab have problems with hard drives. If three computers are selected at random for inspection, what is the probability that none of them has hard drive problems? [0.2] 13. The following table give a two-way classification of all graduates of a college in year 2002 Employed Unemployed Male 179 72 Female 109 49 a. If a person is selected at random from these graduates, find the probability that this person is 1. unemployed, [0.2958] 11. a male, [0.6137] employed given that the person is a female, [0.6899] IV. a male who is employed, [0.4377] V. a male given the person is employed. [0.6215] Are the events employed and unemployed mutually exclusive? What about the events unemployed and male? Why or why not? Are the events female and unemployed independent? Why or why not? b. c. Q2. (b) A spyware is trying to break into system by guessing 100 million (100,000,000) different passwords. Find the probability that it will guess the password and break in if by rules, the password must consists of (i) 6 different upper-case letters, (2 marks) (ii) any 6 letters, upper- or lower-case, and it is case-sensitive, (2 marks) (iii) any 6 characters including letters and digits. (2 marks) (c) A computer program consists of two blocks written independently by two different programmers. The first block has an error with probability 0.1. The second block has an error with probability 0.2. If the program returns an error, find the probability that there is an error in both blocks