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

If a,b are chosen from {1,2,3,4,5,6,7} randomly with replacement. The probability that lim_(x to0) ((a^x+b^x)/2)^(2//x)=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:

If p and q are chosen randomly from the set {1, 2, 3, 4, 5} with replacement. Find the probability that the roots of the equation x^(2) + px + q = 0 are equal.

If P and Q 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 + px + q = 0 are real.