A) \[\frac{1}{20}\]
B) \[\frac{11}{20}\]
C) \[\frac{1}{3}\]
D) \[\frac{3}{20}\]
Correct Answer: B
Solution :
| [b] Given equation |
| \[x+\frac{100}{x}>50\] |
| \[\Rightarrow {{x}^{2}}-50x+100>0\Rightarrow {{(x-25)}^{2}}>525\] |
| \[\Rightarrow x-25<-\sqrt{(525)}\] or \[x-25>\sqrt{(525)}\] |
| \[\Rightarrow x<25-\sqrt{(525)}\] or \[x>25+\sqrt{(525)}\] |
| As x is positive integer and \[\sqrt{(525)}=22.91,\] we must have |
| \[x\le 2\] or \[x\ge 48\] |
| Let E be the event for favourable cases and S be the sample space. |
| \[\therefore \,\,\,\,\,\,E=\{1,\,\,2,\,\,48,\,\,49,\,...100\}\] |
| \[\therefore n(E)=55\] and \[n(S)=100\] |
| Hence the required probability |
| \[P(E)=\frac{n(E)}{n(S)}=\frac{55}{100}=\frac{11}{20}\] |
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