Question

Consider $5$ independent Bernoulli's trials each with probability of success $p$. If the probability of at least one failure is greater then or equal to $31/32$, then $p$ lies in the interval

• A. $[11/12,1]$
• B. $[1/2,3/4]$
• C. $[3/4,11/12]$
• D. $[0,1/2]$

Answer 1

The correct option is D $[0,1/2]$

$p(x=r)={}^5{c}_r{p}^r{q}^{5-r}$

$1-p(x=5)\ge 31/32$

$p^5\le 1/32$

$p\le 1/2$