Question

Given that the sum of two non-negative quantities is 200, the probability that their product is not less than $\frac{3}{4}$ times their greatest product value is:

• A. $\frac{99}{200}$
• B. $\frac{101}{200}$
• C. $\frac{87}{100}$
• D. none of these

Answer 1

The correct option is B $\frac{101}{200}$

Let x and y be the non - negative integers since x + y = 200
$\therefore (xy{)}_{max}=100\times 100=10000(x{y}_{max}atx=y)Now,xy\ge \frac{3}{4}\times 10000\Rightarrow x(200-x)\ge 7500\Rightarrow x^2-200x+7500\le 0\Rightarrow 50\le x\le 150$
So favourable number of ways = 150 - 50 + 1 = 101
Total number of ways = 200
Hence, required probability $=\frac{101}{200}$