Need a step-by-step solution for Q7,8,9 and 10.

At a certain university, 42% of the students are women and 18% of the students are engineering majors. Of the engineers, 22% are women. (a) If a student at this university is selected at random, what is the probability that the selected person is a woman engineering major? (b) If a student at this university is selected at random, what is the probability that the selected person is either a woman or an engineering major? B. A bag contains 10 sweets. 7 are blue and 3 are red. You picked two at random. (a] What is the probability that both sweets are blue if the sweets are drawn with replacement? (b) What is the probability that both sweets are blue if the sweets are drawn without replacement? Page 4 9. At a particular university, 44% of the students are freshmen, 25% are sophomores, 16% are juniors, and 15% are seniors. Of the freshmen, 35% have not declared a major. Of the sophomores, 25% have not declared a major. Of the juniors, 10% have not declared a major, and of the seniors, 3% have not declared a major. (a] If a student is chosen at random, what's the probability that this student has not declared a major? (b) Given that a randomly selected student has not declared a major, what's the probability that this student is a freshman? 10. I roll a fair six-sided die repeatedly until a number less than 3 is observed. What is the probability that I roll the die at least three times (including the time that a number less than 3 is observed)? Hint: For instance, I roll a fair die. The first time I observe 5. It's not less than 3, so I continue. The second time I observe 2. Then I stop since 2 is less than 3. I rolled the fair die two times in this random experiment