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Three randomly choosen non negative intergers 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) $\frac{5}{11}$

Option C

Sample space $\rightarrow^{12}C_{2}$

Number of possibilities 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

$\therefore Probability=\frac{36}{66}=\frac{6}{11}$

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