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

Let X be the random variable denoting the number of stations having problem out of 4.

Then, X ~ Bin(4, p), p = 3/32 = 0.09375

a) Hence, P(X >= 1) = 1 - P(X = 0) = 1 - 0.6745 = 0.3255. (Ans).

b) P(X = 1) = 0.2791. (Ans).

c) P(X = 3) = 0.0030. (Ans).

d) P(X = 0) = 0.6745. (Ans).

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