At a college, 65% of courses have final exams and 42% of courses require research papers. Suppose that 31% of courses have a research paper and a final exam.Part (a)Find the probability that a course has a final exam or a research paper.Part (b)Find the probability that a course has neither of these two requirements.

In a school, 30 % of the students study math and science, 70 % of the students study science. What is the probability of students studying math, given that the student is already studying science.a42.8%42.8%b23.33%23.33%c40%40%d63.8%63.8%

An examination consists of two papers, Paper1 and Paper2. The probability of failing in paper1is 0.3 and that in paper 2 is 0.2. Given that a student has failed in paper2, the probability of failingin paper1 is 0.6. Find the probability of a student failing in both the papers.

1. Six students who obtained between 50% and 70% for class test 1 must be interviewed. The lecturer goes through the class list alphabetically until she finds the first six students who meets the criterium. Suppose that 13% of all students obtained between 50% and 70% for class test 1.(Round to 3 decimal places and use a point-not a comma).a. Calculate the probability that she needs to go through 85 students to obtain the sample of 6. Blank 1b. Calculate the probability that she needs to go through at least 50 students to obtain the sample of 6. Blank 2

The probability that a first year student entering a certain private college needs neither a developmental math course nor a developmental English is 64% while 25% require a developmental math course and 30% require a developmental English course. Find the probability that a first year student requires both a development math course and a developmental English course.

The chance of a student passing an exam is 20%. The chance of a student passing the exam and getting above 90% marks in it is 5%. GIVEN that a student pass the examination, the probability that the student gets above 90% marks is: