5) A system of 32 remotely operated radar stations is monitoring the airspace ov

Question

5) A system of 32 remotely operated radar stations is monitoring the airspace over the North-West Territories. The Central Command has experienced difficulties with monitoring which are believed to be due to technical problems at 3 stations. However, it is not known which of the 32 stations have problems. Four stations are randomly selected at a time, and a diagnostic test is run. What is the probability that of those four stations, a) at least one has a problem? b) exactly one has a problem? c) exactly three have a problem? d) none has a problem?

Explanation / Answer

Probability that a station has a problem = 3/32

Probability that a station has no problems = 29/32

a) First let us find the probablity that none of the four stations have a problem

= (29/32)4 = 0.6745

=> Probability that atleast one station has a problem = 1 - 0.6745 = 0.3255.

b) The one problem can occur at any of the four stations

Probability that a station has a problem = 3/32

Probability that the other three stations do not have any problems = (29/32)3 = 0.7443

=> Probability that exactly one station has a problem = 4 * 3/32 * 0.7443 = 0.2791

c) The three stations that have problems can come in 4C3 = 4 ways.

Probability that three stations have problems = (3/32)3 = 0.0008

Probability that one station does not have any problem = 29/32

=> Probability that exactly three stations have a problem = 4 * 29/32 * 0.0008 = 0.0029

d) The probability that none of the four stations have a problem = (29/32)4 = 0.6745

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

---

---

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