5 independent Bernoulli trials with success probability p.

Question

5 independent Bernoulli trials with success probability $p$. If $P(	ext{at least one failure})\ge\dfrac{31}{32}$, find the interval for $p$.

Accepted Answer

$$1-p^5\ge\frac{31}{32} \implies p^5\le\frac{1}{32} \implies p\le\frac12$$

So $p\in\left[0,\dfrac12\right]$.

Solutions · 1