Question 1 [25] In a survey conducted among a random sample of students the following observations were made regarding their gender and learning environment preferences during the COVID-lQ pandemic: 168 prefer online learning 202 prefer face to face learning 180 prefer blended learning 34 male students prefer online learning and 70 male students prefer blended learning 106 female students prefer face to face learning Required: a) What is the probability that a female student is chosen? b) What is the probability that a male student prefers face to face learning? c) What is the probability that a student prefers online or blended learning? d) If it's known that the student is female, what is the probability that this student prefers online learning. e) Using a practical example, explain the difference between mutually exclusive events and independent events . Question 2 [25] Suppose that the latest census indicates that for every 10 young people available to work only 4 are employed. Suppose a random sample of 20 young graduates is selected. Required: a) What is the probability that they are all employed? b) What is the probability that none of them are employed? c) What is the probability that at least four are employed? d) What is the probability that at most fifteen are employed? e) What is the probability that the number of young graduates who are employed is greater than ten but less than fifteen? f) What is the expected number of graduates who are not employed? g) What is the standard deviation for the number of graduates who are not employed