“Mr. Khoa has devised a new method for giving bonus points to students in his math class as follows:
What is the probability that you will be chosen to go to the board if you are a student who can solve only easy and medium problems?
What is the probability that you and the male student will receive bonus points?”**
- He randomly selects 4 male students to go to the board and assigns each of them a randomly drawn exercise slip.
- Each selected male student may choose whether or not to invite one female student to solve the problem with him.
- If the solution is correct, the male student — or both the male and the chosen female — receive bonus points. If the solution is incorrect, the male student — or both the male and the female — receive a deduction of 1 point.
- There are 12 problems in total: 6 easy, 4 medium, and 2 difficult, divided into 2 separate rounds.
- The class has 16 male students and 29 female students. Among the male students, assume that 25% are excellent (always solve all problems correctly), 37.5% are unable to solve any problem, and the remaining students can solve only easy and medium problems. Among the 29 female students, 7 always solve all problems correctly, 15 can solve only easy and medium problems, and the remaining cannot solve any problem. Assume that the male students do not know the female students’ ability levels.
What is the probability that you will be chosen to go to the board if you are a student who can solve only easy and medium problems?
What is the probability that you and the male student will receive bonus points?”**
