AIEEE 2011 (Offline)Question 1
Consider $5$ independent Bernoulli's trials each with probability of success $p$. If the probability of at least one failure is greater than or equal to $\frac{31}{32}$, then $p$ lies in the interval :
Probability
Solution
$1-p^5\ge\frac{31}{32}\Rightarrow p^5\le\frac1{32}\Rightarrow p\le\frac12$, so $p\in\left[0,\frac12\right]$.