Final answer:
To find the probability that the product of two positive numbers is greater than 1000 when their sum is 100, we find the range of possible values, solve a quadratic inequality, and calculate the probability. The answer is c. 2/5.
So option (C) is correct.
Step-by-step explanation:
To find the probability that the product of two positive numbers is greater than 1000, we need to consider the possible values of the numbers. Since the sum of the two numbers is 100, let's call one number x and the other number 100-x. We need to find the probability that x (100-x) > 1000. This can be rewritten as -x^2 + 100x > 1000. Rearranging the terms, we get x^2 - 100x + 1000 < 0. To solve this quadratic inequality, we can find the roots of the corresponding quadratic equation: x^2 - 100x + 1000 = 0. The discriminant of this equation is (-100)^2 - 4(1)(1000) = 400. Since the discriminant is positive, the quadratic equation has two distinct real roots. We can find these roots using the quadratic formula: x = [100 ± √(400)]/2 = [100 ± 20]/2 = 60 and 40. Therefore, the probability is the range between these roots divided by the total range of possible values, which is 100. The probability is (60 - 40)/100 = 20/100 = 1/5, which is equivalent to option c. Therefore, the correct answer is c. 2/5.