Consider 5 independent Bernoulli's trials each with probability of success

Question:

Consider 5 independent Bernoulli's trials each with probability of success $\mathrm{p}$. If the probability of at least one failure is greater than or equal to $\frac{31}{32}$, then $\mathrm{p}$ lies in the interval :-

  1. $\left[0, \frac{1}{2}\right]$

  2. $\left(\frac{11}{12}, 1\right]$

  3. $\left(\frac{1}{2}, \frac{3}{4}\right]$

  4. $\left(\frac{3}{4}, \frac{11}{12}\right]$

Correct Option: 1

Solution:

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