Question

Three randomly chosen non-negative integer x, y and z are found to satisfy the equation x + y + z = 10. Then, the probability that z is even, is ______.

Options

• 1/2

• 36/55

• 6/11

• 5/11

Answer 1

Three randomly chosen non-negative integer x, y and z are found to satisfy the equation x + y + z = 10. Then, the probability that z is even, is 6/11.

Explanation:

∵ Sample space = ¹²C₂

Number of possibilities for z is even,

z = 0 `\implies` ¹¹C₁

z = 2 `\implies` ⁹C₁

z = 4 `\implies` ⁷C₁

z = 6 `\implies` ⁵C₁

z = 8 `\implies` ³C₁

z = 10 `\implies` ¹C₁ 

Total possibilities = 36

∴ Required probability = 36/66 = 6/11