2. It is found that a certain type of modem fails to connect (communicate) to th

Question

2. It is found that a certain type of modem fails to connect (communicate) to the host computer on an average of 1 in every 5 attempts (logins). (That is, P(failure in each attempt)-.2.) a. What is the probability that a failure occurs on the 10th attempt? b. What is the probability that the first failure occurs on the 10th attempt? c. What is the probability that the first failure occurs after the 20th attempt? d. What is the probability that the third failure occurs on the 5th attempt? e. What is the probability that there are more than 5 failures in 20 attempts? f. Suppose we improve the quality of this modem so that it fails, on the average, 1 in every 1000 attempts. What is the approximate probability that we see no more than 4 failures among the next 4000 attempts?

Explanation / Answer

a) Here it is given that probability of failure in each attempt = 1/5 = 0.2
So P(failure occurs in 10th attmept) = 0.2
Infact probability of failure in any attempt is 0.2.

b) P(first failure occurs in 10th attempt) = P(success in first 9 attempts) * P(failure in 10th attempt)
= (1 - 0.2)^9 * (0.2)^1 = 0.02684355
So there is 2.68% probability that first failure occurs in 10th attempt.

c) P(first failure occurs after 20th attempt) = P(success in first 20 attempts)
= (1 - 0.2)^20 = 0.01152922

d) P(third failure occurs on the 5th attempt) = P(2 successes and 2 faliures in first 4 attempts) * P(failure in 5th attempt)
= (4*0.8) * (3*0.8) * (2*0.2) * (1*0.2) * 0.2
= 0.12288

So there is 12.288% probability that the third failure occurs on the 5th attempt.

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

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