Out of 500 first year students, 260 passed in the first semester and 210 passed in the second semester. If 170 did not passed in either semester,how many passed in both semesters?

In a class of 80 students, 55 students passed in mathematics and 60 passed in chemistry. 10 stu-dents failed in both mathematics and chemistry. (i) How many students passed in both the subjects ? (ii) How many students passed in exactly one of the two subjects ?

In an examination, there are 500 students, 150 passed the first paper and 350 passed the second paper. 50 students passed both the papers. Find the probability that a student selected at random has failed in both the papers.

100 students appeared for two tests, 60 passed the first, 50 passed the second and 30 passed both. Probability that a student selected at random has failed in both tests is

Out of 100 students, 55 passed in Mathematics and 67 passed in Physics 100 students passed at least one of these two subjects. Find how many students passed in Physics only?