Given that the sum of two non-negative quantities is 200, the probability that their product is not less than `3//4` times their greatest product value is

Options

A. `7//16`
B. `8//16`
C. `9//16`
D. `10//16`

Answer

B

Explanation

Let x and y be the two quantities. When the sum of two non-negative quantities is fixed, the product will be maximum when they are equal.
So, the greatest product =xy=1000 when x=y=100
Now,
`xy lt (3)/(4)xx10000`
`implies xy ge (3)/(4)xx10000`
`implies xy ge 7500`
`implies x(200-x) ge 7500`
`implies x^(2)-200 x + 7500 le 0`
`implies (x-50)(x-150) le 0 implies 50 le x le 150`
`therefore` Favourable number of elementary events =101
Total number of elementary events =200.
Hence, required probability `=(101)/(200)`