Question

Three randomly chosen nonnegative integers x, y and z are found to satisfy the equation x + y + z = 10. Then the probability that z is even is ?

• A. $\frac{1}{2}$
• B. $\frac{36}{55}$
• C. $\frac{6}{11}$
• D. $\frac{5}{11}$

Answer 1

The correct option is C $\frac{6}{11}$

Sample space ${\Rightarrow }^{12}{C}_2$
Number of possiblities for z is even.
$z=0{\Rightarrow }^{11}{C}_{1}z=2{\Rightarrow }^9{C}_{1}z=4{\Rightarrow }^7{C}_{1}z=6{\Rightarrow }^5{C}_{1}z=8{\Rightarrow }^3{C}_{1}z=10{\Rightarrow }^1{C}_1$
Total = 36
$\therefore Probability=\frac{36}{66}=\frac{6}{11}$