Two integers x and y are chosen with replacement out of the set {0, 1, 2, 3, …, 10}. Then find the probability that `|x - y| gt 5`.

Two integers xa n dy are chosen with replacement out of the set {0,1,,2,3 ,10}dot Then find the probability that |x-y|> 5.

Two numbers x and y are chosen at random (without replacement) from among the numbers 1,2,3,2004. The probability that x^3+y^3 is divisible by 3 is (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/4

Two distinct numbers a and b are chosen randomly from the set {2,2^(2),2^(3),….2^(25)} . Then the probability that log_(a)b is an integer is

If pa n dq are chosen randomly from the set {1,2,3,4,5,6,7,8,9, 10} with replacement, determine the probability that the roots of the equation x^2+p x+q=0 are real.

If a and b are chosen randomly from the set consisting of number 1, 2, 3, 4, 5, 6 with replacement. Then the probability that lim_(x to 0)[(a^(x)+b^(x))//2]^(2//x)=6 is

Three numbers are chosen at random without replacement from {1,2,3,....10}. The probability that the minimum of the chosen number is 3 or their maximum is 7 , is:

If a and b are chosen randomly from the set {1,2,3,4} with replacement, then the probability of the real roots of the equation x^(2)+ax+b=0 is:

If a and b are chosen randomly from the set {1,2,3,4} with replacement, then the probability of the real roots of the equation x^2+ax+b=0 is