Question

The sum of two positive numbers is $10.$ The probability that their product is greater than $20$ is

• A. $\frac{1}{9}$
• B. $\frac{4}{9}$
• C. $\frac{5}{9}$
• D. $\frac{19}{20}$

Answer 1

The correct option is C $\frac{5}{9}$

The sum of two positive number whose sum is $10$ are $\left\{\right(1,9\left)\right(2,8\left)\right(3,7\left)\right(4,6\left)\right(5,5\left)\right(6,4\left)\right(7,3\left)\right(8,2\left)\right(9,1\left)\right\}$

Total number is $9$

The number whose sum is $10$ and their product is greater than $20$ is $\left\{\right(3,7\left)\right(4,6\left)\right(5,5\left)\right(6,4\left)\right(7,3\left)\right\}$

Total number is $5$

Now,

Probability $=\frac{5}{9}$