1. In a gathering of students, 40% of students in a class major in EE, 50% major in CS and the remaining 10% major in Math. 20% of Engineering students, 10% of the CS students and 40% of Math students are blond. If a randomly selected student from the class is blond, find the probability that he/she majors in CS.
2. A committee of 7 students is to be formed from 10 EE students, 12 CS students and 8 Math students. It is required that at least two students from each major be on the committee. If all possible committees are equally likely, find the probability of forming a committee with 3 EE students.
3. A manufacturing company manufactures 100 products every day. There is a 5% chance that any of the manufactured products is defective and the products are independent. Consider the 100 products manufactured on a single day.
Find the probability that
(a) only the first and the last products are defective and the rest are good
(b) no more than 2 products are defective
(c) the third defective product happens to be the 60th product
(d) there are two defective products within the first 50 products and two more defective products within the second set of 50 products.
4. A committee of 7 students is to be formed from 10 EE students, 12 CS students and 8 Math students. It is required that at least two students from each major be on the committee. If all possible committees are equally likely, find the probability of forming a committee with 3 EE students.
5. A chip manufacturing company manufactures 60% of its chips by process A and the remaining 40% by process B. It is known that 1% of chips manufactured by process A and 5% of chips manufactured by process B are defective. If randomly selected chip manufactured by the company was found to be good, find the probability that it was manufactured by process B.