A) \[\left( \frac{11}{12},1 \right]\]
B) \[\left( \frac{1}{2},\frac{3}{4} \right]\]
C) \[\left( \frac{3}{4},\frac{11}{12} \right]\]
D) \[\left[ 0,\frac{1}{2} \right]\]
Correct Answer: D
Solution :
Probability of atleast one failure \[=1-\] no failure \[\ge \frac{31}{32}\] \[\Rightarrow 1-{{p}^{5}}\ge \frac{31}{32}\] \[\Rightarrow {{p}^{5}}\ge \frac{1}{32}\] \[\Rightarrow p\ge \frac{1}{2}\] Also \[p\ge 0\] Hence \[p\in \left[ 0,\frac{1}{2} \right]\]
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