3. One hundred missiles have been built for use in national defense. The probabi

Question

3. One hundred missiles have been built for use in national defense. The probability of a successful firing in any one test is 0.95. Assuming independent firings, a) what is the probability that among the first ten firings there will be no more than one failure? b) what is the probability that the first failure occurs at the 3rd firing? c what is the probability that the first failure occurs after the 7th firing? d) what is the probability that the 4th failure occurs at the 10th firing? (Set this up and simplify but do not evaluate.)

Explanation / Answer

Binomial distribution: P(X) = nCx px qn-x

P(success), p= 0.95

P(failure), q = 1 - p =0.05

3. a) P(no more than 1 failure in first 10) = P(0 failure) + P(1 failure)

= 0.9510 + 10x0.05x0.959

= 0.5987 + 0.3151

= 0.9138

b) P(first failure on 3rd firing) = P(first 2 success) x P(failure)

= 0.952 x 0.05

= 0.0451

c) P(first failure after 7th firing) = P(first 7 firings are succesful)

= 0.957

= 0.6983

d) P(4th failure on 10th firing) = P(exactly 3 failures on first 9 firings) x P(failure on 10th firing)

= 9C3 x 0.956 x 0.053 x 0.05

= 84 x 0.956 x 0.054

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.