Consider a 6-sided die with all sides not necessarily equally likely such that probability of an even number is P({2,4,6})=1/2, probability of a multiple of 3 is P({3,6})=1/3, and probability of 1 is P({1})=1/6. Given the above conditions, choose the strongest (most stringent) condition of the following that must always hold about P({5}), the probability of 5

Consider a circle with a circumference of one unit length. Let d < 1/6. Suppose that we independently throw two arcs, each of length d, randomly on this circumference so that each arc is uniformly distributed along the circle circumference. The arc attaches itself exactly to the circumference so that arc of length d exactly covers length d of the circumference. What can be said about the probability that the two arcs do not intersect each other?

The Boolean function obtained by adding an inverter to each and every input of an AND gate is:

What is logically equivalent to “If Kareena and Parineeti go to the shopping mall then it is raining”:

Ram has a fair coin, i.e., a toss of the coin results in either head or tail and each event happens with probability exactly half (1/2). He repeatedly tosses the coin until he gets heads in two consecutive tosses. The expected number of coin tosses that Ram does is

A 1 X 1 chessboard has one (1) square, a 2 X 2 chessboards has five (5) squares. Continuing along this fashion, what is the number of squares on the (regular) 8 X 8 chessboard?

There is a set of 2n people: n male and n female. A good party is one with equal number of males and females (including the one where none are invited). The total number of good parties is

Consider a square of side length 2. We throw five points into the square. Consider the following statements:
(i) There will always be three points that lie on a straight line.
(ii) There will always be a line connecting a pair of points such that two points lie on one side of the line and one point on the other.
(iii) There will always be a pair of points which are at distance at most √2 from each other.
Which of the above is true:

Suppose that f(x) is a continuous function such that 0.4 ≤ f(x) ≤ 0.6 for 0 ≤ x ≤ 1. Which of the following is always true?