A) \[\frac{1}{2}\]
B) \[\frac{36}{55}\]
C) \[\frac{6}{11}\]
D) \[\frac{5}{11}\]
Correct Answer: C
Solution :
| We have, x + y + z = 10 |
| Total number of sample space \[{{=}^{12}}{{C}_{2}}=66\] |
| Number of possibilities of z is even |
| \[z=0{{\Rightarrow }^{11}}{{C}_{1}}\]\[\Rightarrow \,\,\,\,\,\,z=2{{\Rightarrow }^{9}}{{C}_{1}}\]\[\Rightarrow \,\,\,\,\,\,z=4{{\Rightarrow }^{9}}{{C}_{1}}\]\[\Rightarrow \,\,\,\,\,\,z=6{{\Rightarrow }^{5}}{{C}_{1}}\]\[\Rightarrow \,\,\,\,\,\,z=8{{\Rightarrow }^{3}}{{C}_{1}}\] |
| \[\Rightarrow \,\,\,\,\,\,z=10{{\Rightarrow }^{1}}{{C}_{1}}\] |
| Total =11+ 9+7+5+3+1=36, Required probability \[=\frac{36}{66}=\frac{6}{11}\] |
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