A point is randomly selected with uniform probability in the X-Y plane within the rectangle with corners at
(0, 0), (1, 0), (1, 2) and (0, 2). If p is the length of the position vector of the point, the expected value of $${p^2}$$ is

Two n bit binary stings, S1 and, are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of bit positions where the two strings different) is equal to d is

Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is

Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day ?