Engineering
Mathematics
Binomial Probability Theorem
Question
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 :
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Solution
\(1 - {P^5} \ge \frac{{31}}{{32}}\)
\({P^5} \le \frac{1}{{32}}\)
\(P \le \frac{1}{2}\)
\(P \in \left[ {0,\frac{1}{2}} \right]\)