In a class of 70 students, there are 5 students who are better than others and they have double the chance of being placed at the first rank in a test in comparison to other students. Vijay is not among these five. What is the probability that Vijay gets the first rank in the test?

Since, 5 students have double the chance of being first than others; you may consider each of them as 2 and compute the probability. Thus, these 5 are equivalent to 10 and remaining 65 added to this make it 75. These 5 students will have probability of being first as 2/75 and remaining 65 students will have the same probability as 1/75. Thus 65 times 1/75 and 5 times 2/75 make it 1. Vijay is one among the 65 students. This is correct.